Calculating K-connectedness reliability using Steiner bounds

Mathematics of Operations Research

Volumn 21, Issue 4, 1996, Pages 905-921

  Chari, Manoj K ^a   Provan, J Scott ^b  

^a LOUISIANA STATE UNIVERSITY   (United States)

^b The University of North Carolina at Chapel Hill   (United States)

Author keywords

Approximation; Bounds; Network; Reliability

Indexed keywords

APPROXIMATION THEORY; BOUNDARY ELEMENT METHOD; COMPUTATIONAL METHODS; GRAPH THEORY; MATHEMATICAL MODELS; POLYNOMIALS; PROBABILITY; RELIABILITY THEORY;

K CONNECTEDNESS RELIABILITY PROBLEM; STEINER BOUNDS;

OPERATIONS RESEARCH;

EID: 0030282668     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.21.4.905     Document Type: Article

References (20)

1. Ball, M. O., C. J. Colbourn, J. S. Provan (1995). Network reliability. M. O. Ball, T. L. Magnanti, C. L. Monma, G. L. Nemhouser, eds., Handbooks in Operations Research and Management Science: Network Models, Chapter 11, Elsevier, Amsterdam, 673-762.
2. _, J. S. Provan (1982). Bounds on the reliability polynomial for shellable independence systems. SIAM J. Algebraic Discrete Methods 3 166-181.
3. _, _ (1983). Calculating bounds on reachability and connectedness in stochastic networks. Networks 13 253-278.
4. Brecht, T. B., C. J. Colbourn (1988). Lower bounds for two-terminal network reliability. Discrete Appl. Math. 21 185-198.
5. Chari, M. K. (1993). Steiner complexes, matroid ports, and shellability. J. Combin. Theory Ser. B 59 41-68.
6. Colbourn, C. J. (1987). The Combinatorics of Network Reliability, Oxford University Press, New York.
7. _ (1988). Edge-packings of graphs and network reliability. Discrete Math. 72 49-61.
8. _, W. R. Pulleyblank (1989). Matroid Steiner problems, the Tutte polynomial and network reliability. J. Combin. Theory Ser. B 41 20-31.
9. Harms, D. D., M. Kraetzl, C. J. Colbourn, J. S. Devitt (1995). Network Reliability: Experiments with a Symbolic Algebra Environment. CRC Press, Boca Raton.
10. Polesskii, V. P. (1971). A lower boundary for the reliability of information networks, Problems Inform. Transmission 7 165-171.
11. Provan, J. S. (1986). The complexity of reliability computations in planar and acyclic graphs, SIAM J. Comput. 15 694-702.
12. _, M. O. Ball (1983). The complexity of counting cuts and of computing the probability that a graph is connected. SIAM J. Comput, 12 777-788.
13. _, L. J. Billera (1980). Decompositions of simplicial complexes related to diameters of convex polyhedra, Math. Oper. Res. 5 576-594.
14. _, M. K. Chari (1993). Counting problems associated with Steiner trees in graphs, Technical Report UNC/OR TR93-10, Operations Research Department, University of North Carolina, Chapel Hill.
15. Rosenthal, A. (1977). Computing the reliability of complex networks, SIAM J. Appl. Math. 32 384-393.
16. Satyanarayana, A., R. K. Wood (1985). A linear time algorithm for computing k-terminal reliability in series-parallel networks, SIAM J. Comput. 14 818-832.
17. Stanley, R. P. (1977). Cohen-Macaulay complexes. M. Aigner, ed., Higher Combinatorics, Reidel, 51-64.
18. Valiant, L. G. (1979). The complexity of enumeration and reliability problems, SIAM J. Comput. 8 410-421.
19. Van Slyke, R M., H. Frank (1972). Network reliability analysis: Part I, Networks 1 279-290.
20. Vertigan, D. (1990). The computational complexity of Tutte invariants for planar graphs, preprint, Mathematical Institute, Oxford University.