Network Reliability

Handbooks in Operations Research and Management Science

Volumn 7, Issue C, 1995, Pages 673-762

  Ball, Michael O ^a   Colbourn, Charles J ^b   Provan, J Scott ^c  

^a University of Maryland   (United States)

^b UNIVERSITY OF WATERLOO   (Canada)

^c UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77957036347     PISSN: 09270507     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0927-0507(05)80128-8     Document Type: Review

References (458)

1. AboElFotoh, H.M.F., Colbourn, C.J., Series-parallel bounds for the two-terminal reliability problem. ORSA J. Comp. 1 (1989), 205–222.
2. AboElFotoh, H.M.F., Colbourn, C.J., Computing the two-terminal reliability for radio broadcast networks. IEEE Trans. Reliab. R-38 (1989), 538–555.
3. AboElFotoh, H.M.F., Colbourn, C.J., Efficient algorithms for computing the reliability of permutation and interval graphs. Networks 20 (1990), 883–898.
4. Abraham, J.A., An improved algorithm for network reliability. IEEE Trans. Reliab. R-28 (1979), 58–61.
5. Adlakha, V.G., An improved conditional Monte Carlo technique for the stochastic shortest path problem. Management Sci. 32 (1986), 1360–1367.
6. Adlakha, V.G., A Monte Carlo technique with quasirandom points for the stochastic shortest path problem. Am. J. Math. Management Sci. 7 (1987), 325–358.
7. Adlakha, V.G., Kulkarni, V.G., A classified bibliography of research on PERT networks. INFOR 27 (1989), 272–296.
8. Aggarwal, K.K., Integration of reliability and capacity in performance measure of a telecommunication network. IEEE Trans. Reliab. R-34 (1985), 184–186.
9. Aggarwal, K.K., Chopra, Y.C., Bajwa, J.S., Capacity consideration in reliability analysis of communication systems. IEEE Trans. Reliab. R-31 (1982), 177–181.
10. Aggarwal, K.K., Misra, K.B., Gupta, J.S., A fast algorithm for reliability evaluation. IEEE Trans. Reliab. R-24 (1975), 83–85.
11. Aggarwal, K.K., Rai, S., Reliability evaluation in computer-communication networks. IEEE Trans. Reliab. R-30 (1981), 32–35.
12. Agrawal, A., Barlow, R.E., A survey of network reliability and domination theory. Oper. Res. 32 (1984), 478–492.
13. Agrawal, A., Satyanarayana, A., An O(|E|), time algorithm for computing the reliability of a class of directed networks. Oper. Res. 32 (1984), 493–515.
14. Agrawal, A., Satyanarayana, A., Network reliability analysis using 2-connected digraph reductions. Networks 15 (1985), 239–256.
15. Agrawal, D.P., Graph theoretical analysis and design of multistage interconnection networks. IEEE Trans. Comput. C-32 (1983), 637–648.
16. Ahlswede, R., Daykin, D.E., An inequality for the weights of two families of sets, their unions, and their intersections. Z. Wahrscheinl. Geb. 43 (1978), 183–185.
17. Aho, A.V., Hopcroft, J.E., Ullman, J.D., The Design and Analysis of Computer Algorithms. 1974, Addison-Wesley.
18. Aldous, D.J., The random walk construction of uniform spanning trees and uniform labeled trees. SIAM J. Discr. Math. 3 (1990), 450–465.
19. Alexopoulos, C., Maximum flows and critical cutsets in stochastic networks with discrete are capacities. Ph.D. thesis, 1988, University of North Carolina at Chapel Hill, N.C.
20. Alexopoulos, C., State space partitioning methods for stochastic stortest path problems. Tech. Rep. J-93-01, 1993, School of Industrial and Systems Engineering, Georgia Institute of Technology.
21. Alexopoulos, C., Fishman, G.S., Characterizing stochastic flow networks using the Monte Carlo method. Networks 21 (1991), 775–798.
22. Alexopoulos, C., Fishman, G.S., Sensitivity analysis in stochastic flow networks using the Monte Carlo method. Networks 23 (1993), 605–621.
23. Andreatta, G., Shortest path models in stochastic networks. Stochastics Comb. Optimization, 1986, 178–186.
24. Aneja, Y.P., Nair, K.P.K., Maximum expected flow in a network subject to arc failures. Networks 10 (1980), 45–57.
25. Arnborg, S., Proskurowski, A., Linear time algorithms for NP-hard problems restricted to k-trees. Discr. Appl. Math. 23 (1989), 11–24.
26. Assous, J.Y., First and second order bounds for terminal reliability. Networks 16 (1986), 319–329.
27. Ayanoglu, E., I, C.-L., A method of computing the coefficients of the network reliability polynomial. Proc. Globecom89, 1989, 331–337.
28. Bailey, M.P., Constant access systems: a general framework for greedy optimization on stochastic networks. Technical Report, 1991, Department of Operations Research, U.S. Naval Postgraduate School.
29. Bailey, M.P., Kulkarni, V.G., A recursive algorithm for computing exact reliability measures. IEEE Trans. Reliab. R-35 (1986), 36–40.
30. Ball, M.O., Computing network reliability. Oper. Res. 27 (1979), 823–836.
31. Ball, M.O., Complexity of network reliability computations. Networks 10 (1980), 153–165.
32. Ball, M.O., Nemhauser, G.L., Matroids and a reliability analysis problem, Math. Oper. Res. 4 (1979), 132–143.
33. Ball, M.O., Provan, J.S., Bounds on the reliability polynomial for shellable independence systems. SIAM J. Algebraic Discr. Methods 3 (1982), 166–181.
34. Ball, M.O., Provan, J.S., Calculating bounds on reachability and connectedness in stochastic networks. Networks 13 (1983), 253–278.
35. Ball, M.O., Provan, J.S., Properties of systems which lead to efficient computation of reliability. Proc. IEEE Global Telecommunications Conference, 1985, 866–870.
36. Ball, M.O., Provan, J.S., Computing k-terminal reliability in time polynomial in the number of (s, K)-quasicuts. Proc. 4th Army Conf. on Applied Mathematics and Computing, 1987, 901–907.
37. Ball, M.O., Provan, J.S., Disjoint products and efficient computation of reliability. Oper. Res. 36 (1988), 703–716.
38. to appear Ball, M.O., Hagstrom, J.N., Provan, J.S., Threshold reliability of networks with small failure. Networks, 1994.
39. Ball, M., Lin, F., A reliability model applied to emergency service vehicle location. Oper. Res. 41 (1993), 18–36.
40. Ball, M.O., Provan, J.S., Shier, D.R., Reliability covering problems. Networks 21 (1991), 345–358.
41. Ball, M.O., Van Slyke, R.M., Backtracking algorithms for network reliability analysis. Ann. Discr. Math. 1 (1977), 49–64.
42. Barlow, R.E., Set theoretic signed domination for coherent structures. Report ORC 82-1, 1982, Univ. California, Monerey, CA.
43. Barlow, R.E., Iyer, S., Computational complexity of coherent systems and the reliability polynomial. Prob. Engrg. Inf. Sci. 2 (1988), 461–469.
44. To Begin With, Silver Spring, Md.Barlow, R.E., Proschan, F., Statistical Theory of Reliability and Life Testing. 1981.
45. Bauer, D., Boesch, F., Suffel, C., Tindell, R., Combinatorial optimization problems in the analysis and design of probabilistic networks. Stevens Research Report in Mathematics 8202, 1982, Stevens Institute of Technolog, Berkeley, Calif.
46. Beichelt, F., Spross, L., Bounds on the relability of binary coherent systems. IEEE Trans. Reliab. R-38 (1989), 425–427.
47. Beichelt, F., Tittmann, P., A generalized reduction method for the connectedness probability of stochastic networks. IEEE Trans. Reliab. R-40 (1991), 198–204.
48. Bein, W.W., Kamburowski, J., Stallmann, M.F.M., Optimal reduction of directed acyclic graphs. SIAM J. Comput. 21 (1992), 1112–1129.
49. Belovich, S.G., Konangi, V.K., A linear-time approximation method for computing the reliability of a network. Comput. Networks ISDN Syst. 21 (1991), 121–127.
50. Ben-Dov, Y., Optimal testing procedures for special structures of coherent systems. Managenent Sci. 27 (1981), 1410–1420.
51. Bibelnieks, E., Jarvis, J.P., Lakin, R.J., Shier, D.R., Algorithms for approximating the performance of multimode systems. Proc. INFOCOM90, 1990, 741–748.
52. Bienstock, D., An algorithm for reliability analysis of planar graphs. Networks 16 (1986), 411–422.
53. Bienstock, D., Some lattice-theoretic tools for network reliability analysis Math. Oper. Res. 13 (1988), 467–478.
54. Bienstock, D., Asymptotic analysis of some network reliability models. SIAM J. Discr. Math. 1 (1988), 14–21.
55. Biggs, N.L., Algebraic Graph Theory. 1974, Cambridge University Press, Hoboken, N.J.
56. Billera, L.J., Polyhedral theory and commutative algebra. Bachem, A., Grötschel, M., Korte, B., (eds.) Mathematical Programming: The State Of The Art, 1977, Springer-Verlag, 57–77.
57. Billera, L.J., Lee, C.W., The number of faces of polytope pairs and unbounded polyhedra. Eur. J. Comb. 2 (1981), 307–332.
58. Birnbaum, Z.W., Esary, J.D., Modules of coherent binary systems. J. SIAM 13 (1965), 444–462.
59. Birnbaum, Z.W., Esary, J.D., Saunders, S.C., Multi-component systems and structures and their reliability. Technometrics 3 (1961), 55–77.
60. Bixby, R., The minimum number of edges and vertices in a graph with edge-connectivity N and MN-bonds. Networks 5 (1975), 259–298.
61. Blake, J.T., Trivedi, K.S., Multistage interconnection network reliability. IEEE Trans. Comput. C-38 (1989), 1600–1603.
62. Blake, J.T., Trivedi, K.S., Reliability analysis of interconnection networks using hierarchical composition. IEEE Trans. Reliab. R-38 (1989), 111–119.
63. Bodin, L., Approximation to system reliability using a modular decomposition. Technometrics, 12, 1970, 335.
64. Boesch, F.T., Synthesis of reliable networks — a survey. IEEE Trans. Reliab. R-35 (1986), 240–246.
65. Boesch, F.T., Satyanarayana, A., Suffel, C.L., Some alternate characterizations of reliability domination. Prob. Engrg. Inf. Sci. 4 (1990), 257–276.
66. Boesch, F.T., Satyanarayana, A., Suffel, C.L., Least reliable networks and the reliability domination. IEEE Trans. Commun. 38 (1990), 2004–2009.
67. Bose, R., Taka, M., Hamilton, C., (eds.) Dependability of Network Services, IEEE Commun. Mag., 1993, 31.
68. Botting, C., Rai, S., Agrawal, D.P., Reliability computation of multistage interconnection networks. IEEE Trans. Reliab. R-38 (1989), 138–145.
69. Brecht, T.B., Colbourn, C.J., Lower bounds for two-terminal network reliability. Discr. Appl. Math. 21 (1988), 185–198.
70. Brecht, T.B., Colbourn, C.J., Improving reliability bounds in computer networks. Networks 16 (1986), 369–380.
71. Brecht, T.B., Colbourn, C.J., Multiplicative improvements in reliability bounds. Networks 19 (1989), 521–530.
72. Broder, A., Generating random spanning trees. Proc. Symp. Foundations of Computer Science, 1989, IEEE, 442–447.
73. Brooks, R.L., Smith, C.A.B., Stone, A.H., Tutte, W.T., The dissection of rectangles into squares. Duke Math. J. 7 (1940), 312–340.
74. Brown, J.I., Colbourn, C.J., A set system polynomial with reliability and coloring applications. SIAM J. Discr. Math. 1 (1988), 151–157.
75. to appear Brown, J.I., Colbourn, C.J., Log concavity and the reliability polynomial. 1994.
76. Brown, J.I., Colbourn, C.J., Roots of the reliability polynomial. SIAM J. Discr. Math. 5 (1992), 571–585.
77. Brown, J.I., Colbourn, C.J., Devitt, J.S., Network transformations and bounding network reliability. Networks 23 (1993), 1–17.
78. Brown, D.B., A computerized algorithm for determining the reliability of redundant configurations. IEEE Trans. Reliab. R-20 (1971), 121–124.
79. Bukowski, J.V., On the determination of large scale system reliability. IEEE Trans. Syst. Man Cybern. SMC-12 (1982), 538–548.
80. Burt, J.M. Jr., Gaver, D.P., Perlas, M., Simple stochastic networks: some problems and procedures. Nav. Res. Logist. Q. 17 (1970), 439–460.
81. Burt, J.M. Jr., Garman, M.B., Monte Carlo techniques for stochastic PERT network analysis. INFOR 9 (1971), 248–262.
82. Burt, J.M. Jr., Garman, M.B., Conditional Monte Carlo: A simulation technique for stochastic network analysis. Managenent Sci. 18 (1971), 207–217.
83. Busacker, R.G., Gowen, P.J., A procedure for determining a family of minimal cost flow patterns. ORO Research Report 15, 1961, Johns Hopkins University.
84. Buzacott, J.A., A recursive algorithm for finding reliability measures related to the connection of nodes in a graph. Networks 10 (1980), 311–327.
85. Buzacott, J.A., The ordering of terms in cut-based recursive disjoint products. IEEE Trans. Reliab. R-32 (1983), 472–474.
86. Buzacott, J.A., Node partition formula for directed graph reliability. Networks 17 (1987), 227–240.
87. Buzacott, J.A., Chang, J.S.K., Cut-set intersections and node partitions. IEEE Trans. Reliab. R-33 (1984), 385–389.
88. Caccetta, L., Kraetzl, M., Blocking probabilities of certain classes of channel graphs. Kulli, V.R., (eds.) Advances in Graph Theory, 1991, Vishwa International, 70–103.
89. Carey, M., Hendrickson, C., Bounds on expected performance with links subject to failure. Networks 14 (1984), 439–456.
90. Carrasco, E.H., Colbourn, C.J., Reliability bounds for networks with statistical dependence. Proc. INFOCOM86, Miami, 1986, 290–292.
91. Chari, M.K., Steiner complexes, matroid ports, and K-connectedness reliability. J. Comb. Theor. (B) 59 (1993), 41–68.
92. preprint Chari, M.K., Feo, T.A., Provan, J.S., A computational study of wye-delta bounds for (s, t)-connectedness reliability. 1990, University of North Carolina, Delhi.
93. Charnes, A., Cooper, W.W., Thompson, G.L., Critical path analysis via chance constrained and stochastic programming. Oper. Res. 12 (1964), 460–470.
94. Chiou, S.-N., Li, V.O.K., Reliability analysis of a communication network with multimode components. IEEE Trans. Sel. Areas Commun. SAC-4 (1986), 1156–1161.
95. Clausen, J., Hansen, L.A., Finding k edge-disjoint spanning trees of minimum total weight in a network: an application of matroid theory. Math. Program. Study 13 (1980), 88–101.
96. Clements, G.F., Lindström, B., A generalization of a combinatorial theorem of Macaulay. J. Comb. Theor. 7 (1968), 230–238.
97. Clingen, C.T., A modification of Fulkerson's PERT algorithm. Oper. Res. 12 (1964), 629–632.
98. Colbourn, C.J., The Combinatorics of Network Reliability. 1987, Oxford University Press.
99. Colbourn, C.J., Network resilience. SIAM J. Algebraic Discr. Methods, 8, 1987, 404–409.
100. Colbourn, C.J., Edge-packings of graphs and network reliability. Discr. Math. 72 (1988), 49–61.
101. Colbourn, C.J., Network reliability: numbers or insight?. Ann. Oper. Res. 33 (1991), 87–93.
102. Colbourn, C.J., A note on bounding k-terminal reliability. Algorithmica 7 (1992), 303–307.
103. Colbourn, C.J., Day, R.P.J., Nel, L.D., Unranking and ranking spanning trees of a graph. J. Algorithms 10 (1989), 271–286.
104. Colbourn, C.J., Devitt, J.S., Harms, D.D., Kraetzl, M., Renormalization for channel graphs. Acta. XI Congr. de Metodologias en Ingenieria de Sistemas, Santiago, Chile, 1991, 171–174.
105. to appear Colbourn, C.J., Devitt, J.S., Harms, D.D., Kraetzl, M., Assessing reliability of multistage interconnection networks. 1994.
106. Colbourn, C.J., Elbert, M., Litvak, E., Weyant, T., Performability analysis of large-scale packet-switching networks. Proc. Int. Conf. on Communications (SUPERCOMM/ICC), Chicago, 1992, 416–419.
107. Colbourn, C.J., Elmallah, E.S., Reliable assignments of processors to tasks and factoring on matroids. Discr. Math. 114 (1993), 115–129.
108. Colbourn, C.J., Harms, D.D., Bounds for all-terminal reliability in computer networks. Networks 18 (1988), 1–12.
109. Colbourn, C.J., Harms, D.D., Myrvold, W.J., Reliability polynomials can cross twice. J. Franklin Inst. 330 (1993), 629–633.
110. Colbourn, C.J., Litvak, E.I., Bounding network reliability by graph transformations. Roberts, F., Hwarg, F., Monma, C., (eds.) Reliability of Computer and Communications Networks, 1991, AMS/ACM, Oxford, New York, 91–104.
111. Colbourn, C.J., Lomonosov, M.V., Renewal networks: connectivity and reliability on a time interval. Probab. Engrg. Inf. Sci. 5 (1991), 361–368.
112. Colbourn, C.J., Nel, L.D., Using and abusing bounds for network reliability. Proc. IEEE Telecommunications Conference (Globecom90), 1990, IEEE Press, 663–667.
113. to appear Colbourn, C.J., Nel, L.D., Boffey, T.B., Yates, D.F., Probabilistic estimation of damage from fire spread. 1994.
114. to appear Colbourn, C.J., Provan, J.S., Vertigan, D.L., The complexity of computing the Tutte polynomial on transversal matroids. 1994.
115. Colbourn, C.J., Pulleyblank, W.R., Matroid Steiner problems, the Tutte polynomial and network reliability. J. Comb. Theor. B41 (1989), 20–31.
116. Corea, G.A., Kulkarni, V.G., Minimum cost routing on stochastic networks. Networks 18 (1990), 527–536.
117. Cox, D.R., The use of complex probability in the theory of stochastic processes. Proc. Camb. Philos. Soc., 51, 1955, 313–319.
118. Crapo, H.H., A higher invariant for matroids. J. Comb. Theor. 2 (1967), 406–417.
119. Daneshmand, M., Savolaine, C., Measuring outages in telecommunications switched networks. IEEE Commun. Mag. 31 (1993), 34–38.
120. Daykin, D.E., A simple proof of the Kruskal-Katona theorem. J. Comb. Theor. A 17 (1974), 252–253.
121. Dean, P., A new Monte Carlo method for percolation probabilities on a lattice. Proc. Camb. Philos. Soc., 59, 1963, 397–410.
122. deMercado, J., Spyratos, N., Bowen, B.A., A method for calculation of network reliability. IEEE Trans. Reliab. R-25 (1976), 71–76.
123. Devitt, J.S., Colbourn, C.J., On implementing an environment for investigating network reliability. Computer Science and Operations Research, 1992, Pergamon Press, 159–173.
124. Dirac, G.A., Short proof of Menger's theorem. Mathematika 13 (1966), 42–44.
125. Dodin, B.M., Approximating the distribution function in stochastic networks. Computers and Oper. Res. 12 (1985), 207–223.
126. Dodin, B.M., Bounding the project completion time distribution in PERT networks. Oper. Res. 33 (1985), 862–881.
127. Dodin, B.M., Elmaghraby, S.E., Approximating the criticality indices of the activities in PERT networks. Oper. Res. 32 (1984), 493–515.
128. Dotson, W.P., Gobien, J.O., A new analysis technique for probabilistic graphs. IEEE Trans. Circuits Syst. CAS-26 (1979), 855–865.
129. Douilliez, P., Jamoulle, E., Transportation networks with random arc capacities. R.A.I.R.O. 3 (1972), 45–49.
130. Duffin, R.J., Topology of series-parallel networks. J. Math. Anal. Appl. 10 (1965), 303–318.
131. Easton, M.C., Wong, C.K., Sequential destruction method for Monte Carlo evaluation of system reliability. IEEE Trans. Reliab. R-29 (1980), 27–32.
132. Edmonds, J., Minimum partition of a matroid into independent subsets. J. Res. Nat. Bur. Stand. 69B (1965), 67–72.
133. Edmonds, J., Optimum branchings. J. Res. Nat. Bur. Stand. 71B (1967), 233–240.
134. Edmonds, J., Matroid partition. Dantzig, G.B., Viennott, A.F., (eds.) Mathematics of the Decision Sciences, 1968, American Mathematical Society, 335–345.
135. Edmonds, J., Edge-disjoint branchings. Rustin, R., (eds.) Combinatorial Algorithms, 1972, Algorithmics Press, 91–96.
136. Edmonds, J., Karp, R.M., Theoretical improvements in algorithmic efficiency for network flow problems. J. ACM 19 (1972), 248–264.
137. Elmaghraby, S.E., Activity Networks: Project Planning and Control by Network Models. 1977, J. Wiley & Sons.
138. Elmaghraby, S.E., On the expected duration of PERT-type networks. Managenent Sci. 13 (1967), 299–306.
139. Elmaghraby, S.E., The estimation of some network parameters in the PERT model of activity networks: review and critique. Słowiński, R., Weglarz, J., (eds.) Advances in Project Scheduling, 1989.
140. Elmaghraby, S.E., Kamburowski, J., Stallmann, M.F.M., On the reduction of acyclic digraphs and its applications. OR Report 233, Oper. Res. Ser., 1989, North Carolina State University.
141. El Mallah, E.S., Colbourn, C.J., Reliability of δ-Y networks. Proc. 16th Southeastern Conf. on Combinatorics, Graph Theorym, Computing, 1985, 49–54.
142. Elperin, T., Gertsbakh, I., Lomonosov, M.V., Network reliability estimation using graph evolution models. IEEE Trans. Reliab. R-40 (1991), 572–581.
143. Epifanov, G.V., Reduction of a plane graph to an edge by a star-triangle transformation. Sov. Math. Dokl. 166 (1966), 13–17.
144. Erdös, P., Renyi, A., On random graphs I. Publ. Math. Debrecen 6 (1959), 290–297.
145. Erdös, P., Renyi, A., On the evolution of random graphs. Magyar Tud. Akad. Mat. Kutató Int. Közl. 5 (1960), 17–61.
146. Esary, J.D., Proschan, F., Coherent structures of non-identical components. Technometrics 5 (1963), 191–209.
147. Evans, J.R., Maximum flow in probabilistic graphs — the discrete case. Networks 6 (1976), 161–183.
148. Even, S., Tarjan, R.E., Network flow testing and graph connectivity. SIAM J. Comput. 4 (1975), 507–518.
149. Feo, T.A., Johnson, R., Partial factoring: an efficient algorithm for approximating two-terminal reliability on complete graphs. IEEE Trans. Reliab. R-39 (1990), 290–295.
150. Feo, T.A., Provan, J.S., Delta-wye transformations and the efficient reduction of two-terminal planar graphs. Oper. Res. 41 (1993), 572–582.
151. Fisher, D.D., Saisi, D., Goldstein, W.M., Stochastic PERT networks: OP diagrams, critical paths and the project completion time. Comput. Oper. Res. 12 (1985), 471–482.
152. Fishman, G.S., Estimating network characteristics in stochastic activity networks. Managenent Sci. 31 (1985), 579–593.
153. Fishman, G.S., A comparison of four Monte Carlo methods for estimating the probability of (s, t)-connectedness. IEEE Trans. Reliab. R-35 (1986), 145–155.
154. Fishman, G.S., A Monte Carlo sampling plan for estimating network reliability. Oper. Res. 34 (1986), 581–594.
155. Fishman, G.S., A Monte Carlo sampling plan for estimating reliability parameters and related functions. Networks 17 (1987), 169–186.
156. Fishman, G.S., The distribution of maximum flow with applications to multistate reliability systems. Oper. Res. 35 (1987), 607–618.
157. Fishman, G.S., Estimating the s-t reliability function using importance and stratified sampling. Oper. Res. 37 (1989), 462–473.
158. Fishman, G.S., Monte Carlo estimation of the maximum flow distribution in a network with discrete stochastic arc capacity levels. Nav. Res. Logist. Q. 36 (1989), 829–849.
159. Fishman, G.S., How errors in component reliability affect system reliability. Oper. Res. 38 (1990), 728–732.
160. Fishman, G.S., Kulkarni, V.G., Improving Monte Carlo efficiency by increasing variance. Report UNC/OR/TR 90-21, 1990, University of North Carolina, N.C., Raleigh, N.C.
161. Fishman, G.S., Kulkarni, V.G., Bounds on conditional reliability. Report UNC/OR/TR 90-22, 1991, University of North Carolina, N.C.
162. Fishman, G.S., Shaw, T.D., Evaluating reliability of stochastic flow networks. Probab. Engrg. Inf. Sci. 3 (1989), 493–509.
163. Flanagan, T., Fiber Network Survivability. IEEE Commun. Mag. 28 (1990), 46–53.
164. Fong, C.C., Buzacott, J.S., An algorithm for symbolic reliability calculation with pathsets or cutsets. IEEE Trans. Reliab. R-36 (1987), 34–37.
165. Feng, H., Chan, S.-P., A method of reliability evaluation for computer-communication networks. Proc. 1990 IEEE Int. Symp. on Circuits and Systems, 1990, 2682–2684.
166. Ford, L.R., Fulkerson, D.R., Flows in Networks. 1962, Princeton University Press.
167. Frank, H., Shortest paths in probabilistic networks. Oper. Res. 17 (1969), 583–599.
168. Frank, H., Chou, W., Network properties of the ARPA computer network. Networks 4 (1974), 213–239.
169. Frank, H., Frisch, I.T., Communication, Transmission and Transportation Networks. 1971, Addison-Wesley.
170. Frank, H., Hakimi, S.L., Probabilistic flow through a communications network. IEEE Trans. Circuit Theor CT-12 (1965), 413–414.
171. Frank, H., Kahn, R.E., Kleinrock, L., Computer Communication Network Design-Experience with Theory and Practice. AFIPS Conf. Proc., 40, 1972, 255–270.
172. Frank, O., Gaul, W., On reliability in stochastic graphs. Networks 12 (1982), 119–126.
173. Frankl, P., A new short proof for the Kruskal-Katona theorem. Discr. Math. 48 (1984), 327–329.
174. Fratta, L., Montanari, U.G., A recursive method based on case analysis for computing network terminal reliability. IEEE Trans. Commun. COM-26 (1978), 1166–1177.
175. Fratta, L., Montanari, U.G., A Boolean algebra method for computing the terminal reliability in a communication network. IEEE Trans. Circuit Theor. CT-20 (1973), 203–211.
176. Frisch, H.L., Hammersley, J.M., Welsh, D.J.A., Monte Carlo estimates of percolation probabilities for various lattices. Phys. Rev. 126 (1962), 949–951.
177. Fu, Y., Yau, S.S., A note on the reliability of communication networks. J. SIAM 10 (1962), 469–474.
178. Fujishige, S., A capacity-rounding algorithm for the minimum cost circulation problem: a dual framework of the Tardos algorithm. Math. Program. 35 (1986), 298–308.
179. Fulkerson, D.R., Expected critical path lengths in PERT Networks. Oper. Res. 10 (1962), 808–817.
180. Fulkerson, D.R., Networks, frames, blocking systems. Dantzig, G.B., Viennott, A.F., (eds.) Mathematics of the Decision Sciences, 1968, American Math. Society, 303–334.
181. Fulkerson, D.R., Blocking and anti-blocking pairs of polyhedra. Math. Program. 1 (1971), 168–194.
182. Fulkerson, D.R., Packing rooted directed cuts in a weighted directed graph. Math. Program. 6 (1974), 1–13.
183. Fulkerson, D.R., Harding, G.H., On edge-disjoint branchings. Networks 6 (1976), 97–104.
184. Gadasin, V., Reliability of communication networks represented by semi-oriented graphs. Engrg. Cybern. 11 (1973), 66–76.
185. Gadasin, V., Reliability of networks with semi-oriented structure. Engrg. Cybern. 14 (1976), 98–104.
186. Gaebler, R., Chen, R., An efficient algorithm for enumerating states of a system with multimode unreliable components. Technical Report, 1987, US Sprint.
187. Garey, M.R., Johnson, D.S., Computers and Intractability: A Guide to the Theory of NP-complete/ness. 1979, Freeman, Overland Park, Kans.
188. Gavish, B., Altinkemer, K., Backbone Network Design Tools with Economic Tradeoffs. ORSA J. Comput 2 (1990), 236–252.
189. Gilbert, E.N., Random graphs. Ann. Math. Stat. 30 (1959), 1141–1144.
190. Gomory, R.E., Hu, T.C., Multiterminal network flows. SIAM J. Applied Math. 9 (1961), 551–570.
191. Gondran, M., Minoux, M., Graphs and Algorithms. 1984, Wiley-Interscience, San Francisco, Calif.
192. Greene, C., Kleitman, D.J., Proof techniques in the theory of finite sets. Rota, G.-C., (eds.) Studies in Combinatorics, 1978, MAA, 22–79.
193. Grimmett, G.R., Welsh, D.J.A., Flow in networks with random capacities. Stochastics 7 (1982), 205–229.
194. Grötschel, M., Lovász, L., Schrijver, A., The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1 (1981), 169–197.
195. Hagstrom, J.N., Combinatorial Properties for Directed Network Reliability with a Path Length Criterion. Technical Report 82-14, 1983, College of Business Administration, University of Illinois.
196. Hagstrom, J.N., Using the decomposition tree of a network in reliability computation. IEEE Trans. Reliab. R-32 (1983), 71–78.
197. Hagstrom, J.N., Using the decomposition tree for directed network reliability computations. IEEE Trans. Reliab. R-33 (1984), 390–395.
198. Hagstrom, J.N., Note on Independence of Arcs in Antiparallel for Network Flow Problems. Networks 14 (1984), 567–570.
199. Hagstrom, J.N., Computational complexity of PERT Problems. Networks 18 (1988), 139–147.
200. Hagstrom, J.N., Computing the probability distribution of project duration in a PERT network. Networks 20 (1990), 231–244.
201. Hagstrom, J.N., Directed network reliability: domination and computing coefficients of the success-marginal expansion. Networks 20 (1990), 65–78.
202. Hagstrom, J.N., Component state dependence and error in reliability computation, preprint. 1990, University of Illinois, Chicago.
203. preprint Hagstrom, J.N., Redundancy, substitutes and complements in system reliability. 1990, University of Illinois, Chicago.
204. Hagstrom, J.N., Kumar, P., Reliability computation on a probabilistic network with Path Length Criterion. Technical Report, 1984, College of Business Administration, University of Illinois, Chicago.
205. Hailperin, T., Best possible inequalities for the probability of a logical function of events. Am. Math. Monthly 72 (1965), 343–359.
206. Halpern, J., The sequential covering problem under uncertainty. INFOR 15 (1977), 76–93.
207. Hammersley, J.M., A Monte Carlo solution of percolation in the cubic crystal. Methods Comput. Phys. 1 (1963), 281–298.
208. Hammersley, J.M., Handscomb, D.C., Monte Carlo Methods. 1964, Methuen & Co. Ltd., Chicago.
209. Hänsler, E., A fast recursive algorithm to calculate the reliability of a communication network. IEEE Trans. Commun. COM-20 (1972), 637–640.
210. Hänsler, E., McAuliffe, G.K., Wilkov, R.S., Exact calculation of computer network reliability. Networks 4 (1974), 95–112.
211. Hariri, S., Raghavendra, C.S., SYREL: A symbolic reliability algorithm based on path cutset methods. IEEE Trans. Comput. C-36 (1987), 1224–1232.
212. Harms, D.D., Colbourn, C.J., The Leggett bounds for network reliability. IEEE Trans. Circuits Syst. CAS-32 (1985), 609–611.
213. Harms, D.D., Colbourn, C.J., Renormalization of two-terminal reliability. Networks 23 (1993), 289–298.
214. Harms, D.D., Colbourn, C.J., Evaluating performability: most probable states and bounds. Proc. Telecomm. Syst. Conf., Nashville, Tenn., 1993.
215. Harms, J.J., Colbourn, C.J., Probabilistic single processor scheduling. Discr. Appl. Math. 27 (1990), 101–112.
216. Hartley, H.O., Wortham, A.W., A statistical theory for PERT critical path analysis. Managenent Sci. 12 (1966), B469–B481.
217. Hayhurst, K.J., Shier, D.R., A factoring approach for the stochastic shortest path problem. Oper. Res. Lett. 10 (1991), 329–334.
218. Hoffman, A.J., Kruskal, J.B., Integral boundary points of convex polyhedra. Kuhn, H.W., Tucker, A.W., (eds.) Linear Inequalities and Related Systems, 1956, Princeton University Press, London, 233–246.
219. Höpfinger, E., Steinhardt, V., On the Exact Evaluation of Finite Activity Networks with Stochastic Durations of Activities. Lecture Notes in Economics and Mathematical Systems, Vol. 117, Optimization and Operations Research, 1976, Springer-Verlag.
220. Hu, T.C., Integer Programming and Network Flows. 1969, Addison-Wesley, New York, N.Y.
221. Huseby, A.B., A unified theory of domination and signed domination with application to exact reliability computations. Statistical Research Report 3, 1984, University of Oslo.
222. Huseby, A.B., Domination theory and the Crapo β-invariant. Networks 19 (1989), 135–149.
223. preprint Huseby, A.B., On regularity, amenability and optimal factoring strategies for reliability computations. 1990, University of Oslo.
224. Hwang, F.K., Odlyzko, A.M., A probability inequality and its application to switching networks. Bell Syst. Tech. J. 56 (1977), 821–826.
225. Hwang, K., Chang, T.P., Combinatorial reliability analysis of multiprocessor computers. IEEE Trans. Reliab. R-31 (1982), 469–473.
226. Jacobs, I.M., Connectivity in probabilistic graphs. Technical Report 356, 1959, Electronics Research Laboratory, MIT.
227. Jaeger, F., Vertigan, D., Welsh, D.J.A., On the computational complexity of the Jones and Tutte polynomials. Math. Proc. Camb. Phil. Soc., 108, 1990, 35–53.
228. Jain, S.P., Gopal, K., An efficient algorithm for computing global reliability of a network. IEEE Trans. Reliab. R-37 (1988), 488–492.
229. Jarvis, J.P., Shier, D.R., An algorithm for approximating the performance of telecommunications systems. Proc. Telecomm. Syst. Conf., Nashville, Tenn., 1993.
230. Jensen, P.A., Bellmore, M., An algorithm to determine the reliability of a complex system. IEEE Trans. Reliab. R-18 (1969), 169–174.
231. Jerrum, M., On the complexity of evaluating multivariate polynomials. Ph.D. thesis, 1981, Department of Computer Science, University of Edinburgh. [Report CST-11-81, Computer Science, University of Edinburgh.]
232. Jewell, W.S., Optimal flow through networks. Interim Report 8, 1958, Massachusetts Institute of Technology.
233. Johnson, R., Network reliability and acyclic orientations. Networks 14 (1984), 489–506.
234. Kamburowski, J., Bounds in temporal analysis of stochastic networks. Found. Control Eng. 10 (1985), 177–189.
235. Kamburowski, J., On the computational complexity of the shortest route and maximum flow problems in stochastic networks. Found. Control Eng. 11 (1986), 167–175.
236. Kamburowski, J., An overview of the computational complexity of the PERT shortest route and maximum flow problems in stochastic networks. World Sci. Publishing, 1987, 187–196.
237. Kamburowski, J., PERT networks under incomplete probabilistic information. Slowinski, R., Weglarz, J., (eds.) Advances in Project Scheduling, 1989, Elsevier Scientific Publishing Co., 433–466.
238. Karmarkar, N., A new polynomial time algorithm for linear programming. Combinatorica 4 (1984), 373–396.
239. Karp, R.M., Reducibility among combinatorial problems. Miller, R.E., Thatcher, J.W., (eds.) Complexity of Computer Computations, 1972, Plenum, 85–103.
240. Karp, R.M., Luby, M., Monte Carlo algorithms for the planar multiterminal network reliability problem. J. Complexity 1 (1985), 45–64.
241. Katona, G., A theorem of finite sets. Erdös, P., Katona, G., (eds.) Theory of Graphs, 1966, Akademia Kiadó, 187–207.
242. Kaustov, V.A., Litvak, Ye.I., Ushakov, I.A., The computational effectiveness of reliability estimates by the method of nonedge-intersecting chains and cuts. Sov J. Comput. Syst. Sci. 24 (1986), 70–73.
243. Kel'mans, A.K., Some problems of network reliability analysis. Autom. Remote Control 26 (1965), 564–573.
244. Kel'mans, A.K., Connectivity of probabilistic networks. Autom. Remote Control 29 (1967), 444–460.
245. Kel'mans, A.K., On estimation of the probabilistic characteristics of random graphs. Autom. Remote Control 32 (1970), 1833–1839.
246. Kel'mans, A.K., Asymptotic formulas for the probability of k-connectedness of random graphs. Theor. Prob. Appl. 27 (1972), 243–254.
247. Kel'mans, A.K., The graph with the maximum probability of remaining connected depends on the edge-removal probability. Graph Theor Newslett. 9 (1979), 2–3.
248. Kel'mans, A.K., On graphs with randomly deleted edges. Acta Math. Acad. Sci. Hung. 37 (1981), 77–88.
249. Kel'mans, A.K., On the analysis and synthesis of probabilistic networks. Selected Transl. Math. Stat. Prob. (AMS) 16 (1985), 127–138.
250. Kesten, H., Surfaces with minimal random weights and maximal flows: a higher-dimensional version of first-passage percolation. Ill. J. Math. 31 (1987), 99–166.
251. Khachiyan, L.G., A polynomial algorithm in linear programming. Sov. Math. Dokl. 20 (1979), 191–194.
252. Kim, Y.H., Case, K.E., Ghare, P.M., A method for computing complex system reliability. IEEE Trans. Reliab. R-21 (1972), 215–219.
253. Kini, N.M., Kumar, A., Agrawal, D.P., Quantitative reliability analysis of redundant multistage interconnection networks. Reliab. Comput. Commun. Networks, 1991, AMS/ACM, Budapest, 153–170.
254. Kirchoff, G., Über die Auflösung der Gleichungen auf welche man bei der Untersuchung der Linearen Verteilung Galvanischer Ströme Geführt wird. Poggendorg's Ann. Phys. Chem. 1847:72 (1958), 497–508. [On the solution of equations obtained from the investigation of the linear distribution of galvanic currents. IRE Trans. Circuit Theor. CT-5, 4–7.]
255. Klein-Hanevelid, K.W., Distributions with known marginals and duality of mathematical programming with application to PERT. Proc. 7th Conf. on Probability Theory, 1985, VNU Sci. Press, 221–236.
256. Klein-Hanevelid, K.W., Robustness against dependence in PERT: an application of duality and distribution with known marginals. Math. Program. Studies, 1986, 153–182.
257. Kleindorfer, G.B., Bounding distributions for a stochastic acyclic network. Oper. Res. 19 (1971), 1586–1601.
258. Kraetzl, M., Colbourn, C.J., Transformations on channel graphs. IEEE Trans. Commun. 41 (1993), 664–666.
259. Krishnamurthy, E.V., Komissar, G., Computer-aided reliability analysis of complicated networks. IEEE Trans. Reliab. R-21 (1972), 86–89.
260. Kruskal, J.B., The number of simplices in a complex. Bellman, R., (eds.) Mathematical Optimization Techniques, 1963, University of California Press, 251–278.
261. Kubat, P., Reliability Analysis for Integrated Networks with Application to Burst Switching. IEEE Trans. Commun. COM-34 (1986), 564–568.
262. Kubat, P., Estimation of Reliability for Communication/Computer Networks-Simulation/Analytic Approach. IEEE Trans. Commun. COM-37 (1989), 927–933.
263. Kubat, P., Smita, U., Masuda, Y., Dynamic Performance Evaluation of Communication/Computer Systems with Highly Reliable Components. Probab. Engrg. Inf. Sci. 2 (1988), 185–213.
264. Kulkarni, V.G., Shortest paths in networks with exponentially distributed arc lengths. Networks 16 (1986), 255–274.
265. Kulkarni, V.G., Minimum spanning trees in undirected networks with exponentially distributed arc weights. Networks 18 (1988), 111–124.
266. Kulkarni, V.G., Generating random combinatorial objects. J. Algorithms 11 (1990), 185–207.
267. Kulkarni, V.G., Adlakha, V.G., Maximum flow in networks with exponentially distributed arc capactities. Stochastic Models 1 (1985), 263–290.
268. Kulkarni, V.G., Adlakha, V.G., Markov and Markov-regenerative PERT networks. Oper. Res. 34 (1987), 769–781.
269. Kulkarni, V.G., Provan, J.S., An improved implementation of conditional Monte Carlo estimation of path lengths in stochastic networks. Oper. Res. 33 (1985), 1389–1393.
270. Kumamoto, H., Tanaka, K., Inoue, K., Efficient evaluation of system reliability by Monte Carlo method. IEEE Trans. Reliab. R-26 (1977), 311–315.
271. Kumamoto, K., Tanaka, K., Inoue, K., Henley, E.J., Dagger sampling Monte-Carlo for system unavailability evaluation. IEEE Trans. Reliab R-29 (1980), 122–125.
272. Lam, Y.F., Li, V.O.K., Reliability modeling and analysis of communications networks with dependent failures. IEEE Trans. Commun. COM-34 (1986), 82–84.
273. Lam, Y.F., Li, V.O.K., An improved algorithm for performance analysis of networks with unreliable components. IEEE Trans. Commun. COM-34 (1986), 496–497.
274. Lawler, E.L., Combinatorial Optimization: Networks and Matroids. 1976, Holt, Rinehart, and Winston.
275. Lee, C.Y., Analysis of switching networks. Bell Syst. Tech. J. 34 (1955), 1287–1315.
276. Lee, S.H., Reliability evaluation of a flow network. IEEE Trans. Reliab. R29 (1980), 24–26.
277. Leggett, J.D., Synthesis of reliable networks. Ph.D. thesis, 1968, Moore School of Engineering, University of Pennsylvania.
278. Leggett, J.D., Bedrosian, S.D., Synthesis of reliable networks. IEEE Trans. Circuit Theor. CT-16 (1969), 384–385.
279. Lehman, A.B., Wye-delta transformations in probabilistic networks. SIAM J. 11 (1963), 773–805.
280. Levy, L.I., Moore, A.H., A Monte Carlo technique for obtaining system reliability confidence limits from test data. IEEE Trans. Reliab. R-16 (1967), 69–72.
281. Li, V.O.K., Silvester, J.A., Performance Analysis of Networks with Unreliable Components. IEEE Trans. Commun. COM-32 (1984), 1105–1110.
282. Lin, P.M., Leon, B.J., Huang, T.C., A new algorithm for symbolic system reliability analysis. IEEE Trans. Reliab. R-25 (1976), 2–15.
283. Litvak, Ye.I., The probability of connectedness of a graph. Engrg. Cybern. 13 (1975), 121–125.
284. Litvak, Ye.I., A generalized triangle-star transformation of properties of complex networks. Engrg. Cybern. 19 (1981), 158–162.
285. Litvak, Ye.I., Two-sided estimates of the minimum cost of a flow in two-terminal networks. Engry. Cybern. 19 (1981), 132–135.
286. Litvak, E.I., A generalized theorem on negative cycles and estimates of the quality of flow transport in a network. Sov. Math. Dokl. 27 (1983), 369–371.
287. Litvak, Ye.I., Ushakov, I.A., Estimation of the parameters of structurally complex systems. Engr. Cybern. 22 (1984), 35–49.
288. Liu, C.I., Chow, Y., Enumeration of connected spanning subgraphs of a planar graph. Acta Math. Hung. 41 (1983), 27–36.
289. Locks, M.O., Recursive disjoint products, inclusion-exclusion, and min-cut approximations. IEEE Trans. Reliab. R-29 (1980), 368–371.
290. Locks, M.O., Recursive disjoint products: a review of three algorithms. IEEE Trans. Reliab. R-31 (1982), 33–35.
291. Lomonosov, M.V., Bernoulli scheme with closure. Probl. Inf. Transm. 10 (1974), 73–81.
292. preprint Lomonosov, M.V., Tender-spot of a reliable network. 1989, Ben Gurion University of the Negev.
293. Lomonosov, M.V., Polesskii, V.P., An upper bound for the reliability of information networks. Probl. Inf. Transm. 7 (1971), 337–339.
294. Lomonosov, M.V., Polesskii, V.P., Lower bound of network reliability. Probl. Inf. Transm 8 (1972), 118–123.
295. Lomonosov, M.V., Polesskii, V.P., Maximum of the connectivity probability. Probl. Inf. Transm. 8 (1972), 324–328.
296. Loui, R.P., Optimal paths in graphs in graphs with stochastic or multidimensional weights. Commun. ACM 26 (1983), 670–676.
297. Lovász, L., On two minimax theorems in graph theory. J. Comb. Theor. B21 (1976), 96–103.
298. Macaulay, F.S., Some properties of enumeration in the theory of modular systems. Proc. London Math. Soc., 26, 1927, 531–555.
299. Malcolm, D.G., Roseboom, J.H., Clark, C.E., Fazar, W., Application of a technique for research and development program evaluation. Oper. Res. 7 (1959), 646–669.
300. Martin, J.J., Distribution of the Time Through a Directed Acyclic Network. Oper. Res. 13 (1965), 46–66.
301. Mata-Montero, E., Reliability of partial k-tree networks. Ph.D. thesis, 1990, University of Oregon.
302. Menger, K., Zur allgemeine Kurventheorie. Fund. Math. 10 (1927), 96–115.
303. Meyer, J.F., Performability: a retrospective and some pointers to the future. Performance Evaluation 14 (1992), 139–156.
304. to appear Mihail, M., Buchsbaum, A.L., Monte Carlo and Markov chain techniques for network reliability and sampling. 1994.
305. Mine, H., Reliability of physical systems. IRE Trans. Circuit Theor. CT-6 (1959), 138–151.
306. Mirchandani, P.B., Shortest distance and reliability of probabilistic networks. Comp. Oper. Res. 3 (1976), 347–355.
307. Mirchandani, P., Soroush, Hossein, Stochastics in Combinatorial Optimization., 1987, World Scientific Publishing Co., 128–177.
308. Misra, K.B., An algorithm for the reliability of redundant networks. IEEE Trans. Reliab. R-19 (1970), 146–151.
309. Misra, K.B., Rao, T.S.M., Reliability analysis of redundant networks using flow graphs. IEEE Trans. Reliab. R-19 (1970), 19–24.
310. Monhor, D., An approach to PERT: application of Dirichlet distribution. Optimization 18 (1987), 113–118.
311. Moore, E.F., The Shortest Path through a Maze. Ann. Comput. Lab. Harvard Univ. 30 (1959), 285–292.
312. Moore, E.F., Shannon, C.E., Reliable circuits using less reliable relays. J. Franklin Inst. 262 (1956), 191–208.
313. Moore, E.F., Shannon, C.E., Reliable circuits using less reliable relays. J. Franklin Inst. 263 (1956), 281–297.
314. Moskowitz, F., The analysis of redundancy networks. AIEE Trans. Commun. Electron. 39 (1958), 627–632.
315. Murray, K., Kershenbaum, A., Shooman, M.L., Communications network reliability analysis: approximations and bounds. Proc. Reliability and Maintainability Symp., 1993, IEEE, 268–275.
316. Myrvold, W.J., Cheung, K.H., Page, L., Perry, J., Uniformly reliable graphs do not always exist. Networks 21 (1991), 417–419.
317. Nádas, A., Probabilistic PERT. IBM J. Res. Dev. 23 (1979), 339–347.
318. Nagamochi, H., Ibaraki, T., Maximum flows in probabilistic networks. Networks 21 (1991), 645–666.
319. Nakazawa, H., Equivalence of a nonoriented line and a pair of oriented lines in a network. IEEE Trans. Reliab. R-28 (1979), 364–367.
320. St. Nash-Williams, C.J.A., Edge-disjoint spanning trees of finite graphs. J. London Math, Soc. 36 (1961), 445–450.
321. St. Nash-Williams, C.J.A., Decomposition of finite graphs into forests. J. London Math. Soc., 39, 1964, 12.
322. Nel, L.D., Colbourn, C.J., Locating a facility in an unreliable network. INFOR 26 (1990), 363–379.
323. Nel, L.D., Colbourn, C.J., Combining Monte Carlo estimates and bounds for network reliability. Networks 20 (1990), 277–298.
324. Nel, L.D., Strayer, H.J., Two-terminal reliability bounds based on edge-packings by cutsets. J. Comb. Math. Comb. Comput. 13 (1993), 3–22.
325. Nelson, A.C., Batts, J.R., Beadles, R.L., A computer program for approximating system reliability. IEEE Trans. Reliab. R-19 (1970), 61–65.
326. Neufeld, E.M., Colbourn, C.J., The most reliable series-parallel networks. Networks 15 (1985), 27–32.
327. von Neumann, J., Probabilistic logics and the synthesis of reliable organisms from unreliable components. Automata Studies, 1956, 43–98.
328. Novikov, V.F., Raikin, A.L., Shufchuk, Yu.B., The effect of reliability on communication delays in a network with maximal flows. Autom. Remote Control 49 (1988), 1613–1619.
329. Onaga, K., Bounds on the average terminal capacity of probabilistic nets. IEEE Trans. Reliab. R 35 (1986), 252–259.
330. Page, L.B., Perry, J.E., A practical implementation of the factoring theorem for network reliability. IEEE Trans. Reliab. R-37 (1988), 259–267.
331. Page, L.B., Perry, J.E., Reliability of directed networks using the factoring theorem. IEEE Trans. Reliab. R-38 (1989), 556–562.
332. Parker, K.P., McCluskey, E.J., Probabilistic treatment of general combinational networks. IEEE Trans. Comput. C-24 (1975), 668–670.
333. Pippenger, N., Developments in ‘The synthesis of reliable organisms from unreliable components’. Proc. AMS Symp. Pure Math., 50, 1990, 311–324.
334. Polesskii, V.P., A lower boundary for the reliability of information networks. Probl. Inf. Transm. 7 (1971), 165–171.
335. Polesskii, V.P., Bounds on probability of connectedness of a random graph. Probl. Inf. Transm. 26 (1990), 75–82.
336. Polesskii, V.P., Bounds on probability of group connectedness of a random graph. Probl. Inf. Transm. 26 (1990), 161–169.
337. Polesskii, V.P., Lower bounds on the probability of connectedness of random graphs generated by 2-connected graphs with a given base spectrum. Probl. Inf. Transm. 28 (1992), 175–183.
338. Politof, T., A characterization and efficient reliability computation of δ-Y reducible networks. Ph.D. thesis, 1983, University of California at Berkeley, Calif.
339. Politof, T., Satyanarayana, A., Efficient algorithms for reliability analysis of planar networks — a survey. IEEE Trans. Reliab. R-35 (1986), 252–259.
340. Politof, T., Satyanarayana, A., Network reliability and inner-four-cycle-free graphs. Math. Oper. Res. 7 (1986), 97–111.
341. Politof, T., Satyanarayana, A., A linear-time algorithm to compute the reliability of planar cube-free networks. IEEE Trans. Reliab. R-39 (1990), 557–563.
342. Prékopa, A., Boros, E., On the existence of a feasible flow in a stochastic transportation network. Oper. Res. 39 (1991), 119–129.
343. Prékopa, A., Boros, E., Lih, K.-W., The use of binomial moments for bounding network reliability. Roberts, F., Hwang, F., Monma, C., (eds.) Reliability of Computer and Communications Networks, 1991, AMS/ACM, 197–212.
344. Provan, G.M., A logic-based analysis of Dempster-Shafer theory. Int. J. Approx. Reason. 4 (1990), 451–495.
345. Provan, J.S., Polyhedral combinatorics and network reliability. Math. Oper. Res. 11 (1986), 36–61.
346. Provan, J.S., Bounds on the reliability of networks. IEEE Trans. Reliab. R-35 (1986), 260–268.
347. Provan, J.S., The complexity of reliability computations in planar and acyclic graphs. SIAM J. Comp. 15 (1986), 694–702.
348. Provan, J.S., Boolean decomposition schemes and the complexity of reliability computations. Roberts, F., Hwang, F., Monma, C., (eds.) Reliability of Computer and Communications Networks, 1991, AMS/ACM, 213–228.
349. Provan, J.S., Ball, M.O., The complexity of counting cuts and of computing the probability that a graph is connected. SIAM J. Comp. 12 (1983), 777–788.
350. Provan, J.S., Ball, M.O., Computing network reliability in time polynomial in the number of cuts. Oper. Res. 32 (1984), 516–526.
351. Provan, J.S., Billera, L.J., Decompositions of simplicial complexes related to diameters of convex polyhedra. Math. Oper. Res. 5 (1980), 579–594.
352. Provan, J.S., Kulkarni, V.G., Exact cuts in networks. Networks 19 (1989), 281–289.
353. Rai, S., A cutset approach to reliability evaluation in communication networks. IEEE Trans. Reliab. R-31 (1982), 428–431.
354. Rai, S., Agrawal, D., (eds.) Distributed Computing Network Reliability, 1990, IEEE Computer Society Press.
355. Rai, S., Agrawal, D., (eds.) Advances in Distributed System Reliability, 1990, IEEE Computer Society Press, Los Alamitos, Calif.
356. Rai, S., Aggarwal, K.K., An efficient method for reliability evaluation of a general network. IEEE Trans. Reliab. R-27 (1978), 206–211.
357. Raman, V., Finding the best edge-packing for two-terminal reliability is NP-hard. J. Comb. Math. Comb. Comput. 9 (1991), 91–96.
358. Ramanathan, A., Colbourn, C.J., Bounds on all-terminal reliability via arc-packing. Ars Combinatoria 23A (1987), 91–94.
359. Ramanathan, A., Colbourn, C.J., Counting almost minimum cutsets and reliability applications. Math. Program. 39 (1987), 253–261.
360. Ramesh, A., Ball, M.O., Colbourn, C.J., Bounding all-terminal reliability in planar networks. Ann. Discr. Math. 33 (1987), 261–273.
361. Resende, L.I.P., Implementation of a factoring algorithm for reliability evaluation of undirected networks. IEEE Trans. Reliab. R-37 (1988), 462–468.
362. Resende, M.G.C., A program for reliability evaluation of undirected networks via polygon-to-chain reductions. IEEE Trans. Reliab. R-35 (1986), 24–29.
363. Ringer, L.J., Numerical operators for statistical PERT critical path analysis. Management Sci. 16 (1969), 136–143.
364. Ringer, L.J., A statistical theory for PERT in which completion times of activities are inter-dependent. Management Sci. 17 (1971), 717–723.
365. Robacker, J.T., Minmax theorems on shortest chains and disjoint cuts of a network. Memo RM-1660-PR, 1956, The Rand Corporation, Los Alamitos, Calif.
366. Robillard, P., Trahan, M., Expected Completion Time in PERT Networks. Oper. Res. 24 (1977), 177–182.
367. Rosenthal, A., A computer scientist looks at reliability computations. Barlow, R.E., Russell, J.B., Singparwalla, N.B., (eds.) Reliability and Fault Tree Analysis, 1975, SIAM, 133–152.
368. Rosenthal, A., Computing the reliability of complex networks. SIAM J. Appl. Math. 32 (1977), 384–393.
369. Rosenthal, A., Frisque, D., Transformations for simplifying network reliability calculations. Networks 7 (1977), 97–111.
370. Roskind, J., Tarjan, R.E., A note on finding minimum cost edge-disjoint spanning trees. Math. Oper. Res. 10 (1985), 701–708.
371. Sahner, R.A., Trivedi, K.S., Performance and reliability analysis using directed acyclic graphs. IEEE Trans. Software Engrg. 10 (1987), 1105–1114.
372. Sanso, B., Gendreau, M., Soumis, F., An algorithm for network dimensioning under reliability consideration. Ann. Oper. Res. 36 (1992), 263–274.
373. Sanso, B., Soumis, F., Communication and Transportation Networks Reliability Using Routing Models. IEEE Trans. Reliab. R-40 (1991), 29–38.
374. Sanso, B., Soumis, F., A Centralized Optimization Routing Model and Applications in Telecommunication Networks. Centre de Recherche sur les Transports Research Report #CRT-657, 1990, Université de Montreal.
375. Sanso, B., Soumis, F., Gendreau, M., On the Evaluation of Telecommunications Network Reliability Using Routing Models. IEEE Trans. Commun. 39 (1991), 1494–1501.
376. Satyanarayana, A., A unified formula for analysis of some network reliability problems. IEEE Trans. Reliab. R-31 (1982), 23–32.
377. Satyanarayana, A., Chang, M.K., Network reliability and the factoring theorem. Networks 13 (1983), 107–120.
378. Satyanarayana, A., Hagstrom, J.N., A new algorithm for the reliability analysis of multi-terminal networks. IEEE Trans. Reliab. R-30 (1981), 325–334.
379. Satyanarayana, A., Hagstrom, J.N., Combinatorial properties of directed graphs useful in computing network reliability. Networks 11 (1981), 357–366.
380. Satyanarayana, A., Khalil, Z., On an invariant of graphs and the reliability polynomial. SIAM J. Alg. Disc. Methods 7 (1986), 399–403.
381. Satyanarayana, A., Prabhakar, A., New topological formula and rapid algorithm for reliability analysis of complex networks. IEEE Trans. Reliab. R-27 (1978), 82–100.
382. Satyanarayana, A., Schoppmann, L., Suffel, C.L., A reliability-improving graph transformation with applications to network reliability. Networks 22 (1992), 209–216.
383. Satyanarayana, A., Wood, R.K., A linear time algorithm for computing k-terminal reliability in series-parallel networks. SIAM J. Comput. 14 (1985), 818–832.
384. Shanthikumar, J.G., Reliability of systems with consecutive minimal cutsets. IEEE Trans. Reliab. 36 (1987), 546–550.
385. Shanthikumar, J.G., Bounding network reliability using consecutive minimal cutsets. IEEE Trans. Reliab. R-37 (1988), 45–49.
386. Shier, D.R., Iterative algorithms for calculating network reliability. Alavi, Y., et al. (eds.) Graph Theory with Applications to Algorithms and Computer Science, 1985, Wiley, 741–752.
387. Shier, D.R., A new algorithm for performance analysis of communication systems. IEEE Trans. Commun. COM-36 (1988), 516–519.
388. Shier, D.R., Network Reliability and Algebraic Structures. 1991, Oxford University Press.
389. Shier, D.R., Algebraic methods for bounding network reliability. Roberts, F., Hwang, F., Monma, C., (eds.) Reliability of Computer and Communications Networks, 1991, AMS/ACM, Oxford, New York, 245–259.
390. Shier, D.R., Spragins, J.D., Exact and approximate dependent failure models for telecommunications networks. Proc. INFOCOM85, 1985, 200–205.
391. Shier, D.R., Valvo, E., Jamison, R., Generating the states of a binary stochastic system. Discr. Appl. Math. 38 (1992), 489–500.
392. Shier, D.R., Whited, D.E., Algebraic methods applied to network reliability problems. SIAM J. Algebraic Discr. Methods 8 (1987), 251–262.
393. Shogan, A.W., Sequential bounding of the reliability of a stochastic network. Oper. Res. 24 (1976), 1027–1044.
394. Shogan, A.W., Bounding distributions for a Stochastic PERT network. Networks 7 (1977), 359–381.
395. Shogan, A.W., A recursive algorithm for bounding network reliability. IEEE Trans. Reliab. R-26 (1977), 322–327.
396. Shogan, A.W., A decomposition algorithm for network reliability analysis. Networks 8 (1978), 231–251.
397. Shogan, A.W., Modular decomposition and reliability computation in stochastic transportation networks having cutnodes. Networks 12 (1982), 255–275.
398. Shooman, A.M., Kershenbaum, A., Methods for communication-network reliability analysis: probabilistic graph reduction. Proc. Symp. on Reliability and Maintainability, 1992, 441–448.
399. Shooman, M.L., Probabilistic Reliability: An Engineering Approach. 1968, McGraw-Hill.
400. Sigal, C.E., The stochastic shortest route problem. Ph.D. Dissertation, 1977, Purdue University, New York, N.Y.
401. Sigal, C.E., Pritsker, A.A.B., Solberg, J.J., The stochastic shortest route problem. Oper. Res. 28 (1980), 1122–1129.
402. Sigal, C.E., Pritsker, A.A.B., Solberg, J.J., The use of cutsets in Monte Carlo analysis of stochastic networks. Math. Comput. Simulation 21 (1980), 376–384.
403. Soh, S., Rai, S., CAREL: Computer aided reliability evaluator for distributed computing networks. IEEE Trans. Parallel Distrib. Syst. 2 (1991), 199–213.
404. Soi, I.M., Aggarwal, K.K., Reliability indices for topological design of computer communication networks. IEEE Trans. Reliab. R-30 (1981), 438–443.
405. Somers, J.E., Maximum flow in a network with a small number of random arc capacities. Networks 12 (1982), 242–253.
406. Spelde, H.G., Bounds for the distribution function of network variables. Proc. 1st Symp. of Operations Research, 3, 1977, University of Heidelberg, 113–123.
407. Sperner, E., Ein Satz über Untermengen einer endlichen Menge. Math. Z. 27 (1928), 544–548.
408. Sperner, E., Über einen kombinatorischen Satz von Macaulay und seine Anwendung auf die Theorie der Polynomideale. Abh. Math. Sem. Univ. Hamburg 7 (1930), 149–163.
409. Spragins, J.D., Dependent failures in data communication systems. IEEE Trans. Commun. COM-25 (1977), 1494–1499.
410. Spragins, J.D., Sinclair, J.C., Kang, Y.J., Jafari, H., Current telecommunication network reliability models: a critical assessment. IEEE Trans. Selected Areas Commun. SAC-4 (1986), 1168–1173.
411. Stanley, R.P., The upper bound conjecture and Cohen-Macaulay rings. Studies Appl. Math. 14 (1975), 135–142.
412. Stanley, R.P., Cohen-Macaulay complexes. Aigner, M., (eds.) Higher Combinatorics, 1977, Reidel, 51–64.
413. Stanley, R.P., Hilbert functions of graded algebras. Adv. Math. 28 (1978), 57–83.
414. Stanley, R.P., Combinatorics and Commutative Algebra. 1983, Birkhäuser Verlag.
415. Stanley, R.P., An introduction to combinatorial commutative algebra. Jackson, D.M., Vanstone, S.A., (eds.) Enumeration and Design, 1984, Academic Press, 3–18.
416. Stepanov, V.E., Combinatorial algebra and random graphs. Theor. Probab. Appl. 14 (1969), 373–399.
417. preprint Strayer, H.J., Colbourn, C.J., Bounding network reliability via surface duality. 1992.
418. to appear Strayer, H.J., Colbourn, C.J., Consecutive cuts and paths, and bounds on k-terminal reliability. 1994.
419. Tardós, E., A strongly polynomial minimum cost circulation algorithm. Combinatorica 5 (1985), 247–256.
420. Tarjan, R.E., A good algorithm for edge-disjoint branching. Inf. Process. Lett. 3 (1974), 51–53.
421. Theologou, O.R., Cartier, J.G., Factoring and reductions for networks with imperfect vertices. IEEE Trans. Reliab. R-40 (1991), 210–217.
422. Tiwari, R.K., Verma, M., An algebraic technique for reliability evaluation. IEEE Trans. Reliab. R-29 (1980), 311–313.
423. preprint Traldi, L., On the star-delta transformation in network reliability. 1994, Lafayette College.
424. preprint Traldi, L., Generalized activities and k-terminal reliability. 1994, Lafayette College.
425. Truemper, K., On the delta-wye reduction of planar graphs. J. Graph Theory 13 (1989), 141–148.
426. Tsuboi, T., Aruba, K., A new approach to computing terminal reliability in large complex networks. Electr. Commun. Japan 58A (1975), 52–60.
427. Tsukiyama, S., Shirakawa, I., Ozaki, H., Ariyoshi, H., An algorithm to enumerate all cutsets of a graph in linear time per cutset. J. ACM 27 (1980), 619–632.
428. Tutte, W.T., On the problem of decomposing a graph into n connected factors. J. London Math. Soc. 36 (1961), 221–230.
429. Ushakov, I., Litvak, Ye.I., An upper and lower estimate of the parameters of two-terminal networks. Engrg. Cybern., 15, 1977.
430. Valiant, L.G., The complexity of computing the permanent. Theor. Comput. Sci. 8 (1979), 189–201.
431. Valiant, L.G., The complexity of enumeration and reliability problems. SIAM J. Comp. 8 (1979), 410–421.
432. Valvo, E.J., Shier, D.R., Jamison, R.E., Generating the most probable states of a communication system. Proc. INFOCOM87, 1987, 1128–1136.
433. Varma, A., Raghavendra, C.S., Reliability analysis of redundant-path interconnection networks. IEEE Trans. Reliab. R-38 (1989), 130–137.
434. Van Slyke, R.M., Monte Carlo methods and the PERT problem. Oper. Res. 11 (1963), 839–860.
435. Van Slyke, R.M., Frank, H., Network reliability analysis: part I. Networks 1 (1972), 279–290.
436. Veeraraghavan, M., Trivedi, K.S., An improved algorithm for symbolic reliability analysis. IEEE Trans. Reliab. R-40 (1991), 347–358.
437. preprint Vertigan, D., The computational complexity of Tutte invariants for planar graphs. 1994, Mathematical Institute, Oxford University.
438. preprint Vertigan, D., Bicycle dimension and special points of the Tutte polynomial. 1994, Mathematical Institute, Oxford University.
439. Vtorova-Karevskaya, B.Ya., Litvak, Ye.I., The reliability of systems admitting two kinds of failures. Engrg. Cybern., 17, 1979.
440. Wagner, D.K., Disjoint (s,t)-cuts in a network. Networks 20 (1990), 361–372.
441. Wald, J.A., Colbourn, C.J., Steiner trees, partial 2-trees, and minimum IFI networks. Networks 13 (1983), 159–167.
442. Wald, J.A., Colbourn, C.J., Steiner trees in probabilistic networks. Microelectron. Reliab. 23 (1983), 837–840.
443. Weiss, G., Stochastic bounds on distributions of optimal value functions with applications to PERT, network flows and reliability. Oper. Res. 34 (1986), 595–605.
444. Welsh, D.J.A., Matroid Theory. 1976, Academic Press.
445. Whipple, F., On a theorem due to F.S. Macaulay. J. London Math. Soc. 8 (1928), 431–437.
446. Whited, D.E., Shier, D.R., Jarvis, J.P., Reliability computations for planar networks. ORSA J. Comput. 2 (1990), 46–60.
447. Whitney, H., A logical expansion in mathematics. Bull. Am. Math. Soc. 38 (1932), 572–579.
448. Willie, R.R., A theorem concerning cyclic directed graphs with applications to network reliability. Networks 10 (1980), 71–78.
449. Wing, O., Demetriou, P., Analysis of probabilistic networks. IEEE Trans. Commun. Tech. COM-12 (1964), 38–40.
450. Wong, R.T., A dual ascent approach for Steiner tree problems on a directed graph. Math. Program. 28 (1984), 271–287.
451. Wood, R.K., Polygon-to-chain reductions and extensions for reliability evaluation on undirected networks. Ph.D. thesis, 1982, University of California at Berkeley, Calif.
452. Wood, R.K., A factoring algorithm using polygon-to-chain reductions for computing k-terminal network reliability. Networks 15 (1985), 173–190.
453. Wood, R.K., Triconnected decomposition for computing K-terminal network reliability. Networks 19 (1989), 203–220.
454. Yang, C.-L., Kubat, P., Efficient computation of most probable states for communication networks with multimode components. IEEE Trans. Commun. COM-37 (1989), 535–538.
455. Yang, C.-L., Kubat, P., An algorithm for network reliability bounds. ORSA J. Comput. 2 (1990), 336–345.
456. Yarlagadda, R., Hershey, J., Fast algorithm for computing the reliability of a communication network. Int. J. Electron. 70 (1991), 549–564.
457. Yoo, Y.B., Deo, N., A comparison of algorithms for terminal-pair reliability. IEEE Trans. Reliab. R-37 (1988), 210–215.
458. Zemel, E., Polynomial algorithms for estimating network reliability. Networks 12 (1982), 439–452.