On the computational complexity of dynamic graph problems

Theoretical Computer Science

Volumn 158, Issue 1-2, 1996, Pages 233-277

  Ramalingam, G ^a   Reps, Thomas ^b  

^a IBM T J WATSON RESEARCH CENTER   (United States)

^b University of Wisconsin Madison   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CALCULATIONS; COMPUTATIONAL METHODS; DATA STRUCTURES; GRAPH THEORY; MATHEMATICAL MODELS; POLYNOMIALS;

COMPLEXITY HIERARCHY; DYNAMIC GRAPH PROBLEMS; INCREMENTAL ALGORITHMS;

COMPUTATIONAL COMPLEXITY;

EID: 0030146097     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/0304-3975(95)00079-8     Document Type: Article

References (46)

1. B. Alpern, R. Hoover, B.K. Rosen, P.F. Sweeney and F.K. Zadeck, Incremental evaluation of computational circuits, in: Proc. of the First Ann. ACM-SIAM Symp. on Discrete Algorithms, San Francisco, CA, 22-24 Jan. 1990 (Society for Industrial and Applied Mathematics, Philadelphia, PA, 1990) 32-42.
2. G. Ausiello, G.F. Italiano, A.M. Spaccamela and U. Nanni, Incremental algorithms for minimal length paths, in: Proc. of the First Ann. ACM-SIAM Symp. on Discrete Algorithms, San Francisco, CA, 22-24 Jan. 1990 (Society for Industrial and Applied Mathematics, Philadelphia, PA, 1990) 12-21.
3. A.M. Berman, M.C. Paull and B.G. Ryder, Proving relative lower bounds for incremental algorithms, Acta Informatica 27 (1990) 665-683.
4. J. Cai and R. Paige, Binding performance at language design time, in: Conf. Record of the Fourteenth ACM Symp. on Principles of Programming Languages, Munich, W. Germany, January 1987 (ACM, New York, NY, 1987) 85-97.
5. J. Cai and R. Paige, Languages polynomial in the input plus output, in: Proc. of the Second Internat. Conf. on Algebraic Methodology and Software Technology (AMAST), Iowa City, Iowa 22-25 May 1991 (1991).
6. M. Carroll and B. Ryder, Incremental data flow update via attribute and dominator updates, in: Conf. Record of the Fifteenth ACM Symp. on Principles of Programming Languages, San Diego, CA, 13-15 January 1988 (ACM, New York, NY, 1988) 274-284.
7. M.D. Carroll, Data flow update via dominator and attribute updates, Ph.D. Dissertation, Rutgers University, New Brunswick, NJ, 1988.
8. G.A. Cheston, Incremental algorithms in graph theory, Ph.D. Dissertation and Tech. Rep. 91, Dept. of Computer Science, University of Toronto, Toronto, Canada, 1976.
9. G.A. Cheston and D.G. Cornell, Graph property update algorithms and their application to distance matrices, INFOR 20(3) (1982) 178-201.
10. T.H. Cormen, C.E. Leiserson and R.L. Rivest, Introduction to Algorithms (MIT Press, Cambridge, MA, 1990).
11. R. Dionne, Etude et extension d'un algorithme de Murchland, INFOR 16(2) (1978) 132-146.
12. J.R. Driscoll, H.N. Gabow, R. Shraiman, and R.E. Tarjan, Relaxed heaps: an alternative to Fibonacci heaps with applications to parallel computation, Commun. ACM 31 (1988) 1343-1354.
13. J. Edmonds and R.M. Karp, Theoretical improvements in algorithmic efficiency for network flow problems, J. ACM 19 (1972) 248-264. As cited in Ref. [45].
14. S. Even and Y. Shiloach, An on-line edge-deletion problem, J. ACM 28(1) (1981) 1-4.
15. S. Even and H. Gazit, Updating distances in dynamic graphs, in: IX Symp. on Operations Research, Osnabrueck, W. Ger., 27-29 Aug. 1984, Methods of Operations Research, Vol. 49, ed. P. Brucker and R. Pauly (Anton Hain, Königstein, 1985) 271-388.
16. S. Goto and A. Sanglovanni-Vincentelli, A new shortest path updating algorithm, Networks 8(4) (1978) 341-372.
17. Y. Gurevich and S. Shelah, Time polynomial in input or output, J. Symbolic Logic 54(3) (1989) 1083-1088.
18. A.K. Halder, The method of competing links, Transportation Sci. 4 (1970) 36-51.
19. R. Hoover, Incremental graph evaluation, Ph.D. Dissertation and Tech. Rep. 87-836, Dept. of Computer Science, Cornell University, Ithaca, NY, 1987.
20. W. Hsieh, A. Kershenbaum and B. Golden, Constrained routing in large sparse networks, in: Proc. IEEE Internat. Conf. on Communications, Philadelphia, PA (1976) 38.14-38.18.
21. C.-C. Lin and R.-C. Chang, On the dynamic shortest path problem, J. Inform. Process. 13(4) (1990) 470-476.
22. P. Loubal, A network evaluation procedure, Highway Res. Record 205 (1967) 96-109.
23. T.J. Marlowe, Data flow analysis and incremental iteration, Ph.D. Dissertation and Tech. Rep. DCS-TR-255, Rutgers University, New Brunswick, NJ, 1989.
24. T.J. Marlowe and B.G. Ryder, An efficient hybrid algorithm for incremental data flow analysis, in: Conf. Record of the Seventeenth ACM Symp. on Principles of Programming Languages, San Francisco, CA, 17-19 Jan. 1990, (ACM, New York, NY, 1990) 184-196.
25. J.D. Murchland, The effect of increasing or decreasing the length of a single arc on all shortest distances in a graph, Tech. Rep. LBS-TNT-26, London Business School, Transport Network Theory Unit, London, UK, 1967.
26. J.D. Murchland, A fixed matrix method for all shortest distances in a directed graph and for the inverse problem, Doctoral dissertation, Universität Karlsruhe, W. Germany.
27. U. Pape, Netzwerk-veraenderungen und korrektur kuerzester weglaengen von einer wurzelmenge zu allen anderen knoten, Computing 12 (1974) 357-362.
28. G. Ramalingam and T. Reps, On the computational complexity of incremental algorithms, TR-1033, Computer Sciences Department, University of Wisconsin, Madison, WI, 1991.
29. G. Ramalingam, Bounded incremental computation, Ph.D. Dissertation and Tech. Rep. TR-1172, Computer Sciences Department, University of Wisconsin, Madison, WI, 1993.
30. J.H. Reif, A topological approach to dynamic graph connectivity, Informat. Process. Lett. 25(1) (1987) 65-70.
31. T. Reps, Optimal-time incremental semantic analysis for syntax-directed editors, in: Conf. Record of the Ninth ACM Symp. on Principles of Programming Languages, Albuquerque, NM, 25-27 January 1982 (ACM, New York, NY, 1982) 169-176.
32. T. Reps, T. Teitelbaum and A. Demers, Incremental context-dependent analysis for language-based editors, ACM Trans. Program. Lang. Syst. 5(3) (1983) 449-477.
33. T. Reps, Generating Language-Based Environments (MIT Press, Cambridge, MA, 1984).
34. T. Reps, C. Marceau and T. Teitelbaum, Remote attribute updating for language-based editors, in: Conf. Record of the Thirteenth ACM Symp. on Principles of Programming Languages, St. Petersburg, FL, 13-15 Jan. 1986 (ACM, New York, NY 1986).
35. T. Reps, Incremental evaluation for attribute grammars with unrestricted movement between tree modifications, Acta Inform. 25 (1988) 155-178.
36. T. Reps and T. Teitelbaum, The Synthesizer Generator: A System for Constructing Language-Based Editors (Springer, New York, NY, 1988).
37. V. Rodionov, The parametric problem of shortest distances, U.S.S.R. Comput. Math. Math. Phys. 8(5) (1968) 336-343.
38. H. Rohnert, A dynamization of the all pairs least cost path problem, in: Proc. of STACS 85: Second Ann. Symp. on Theoretical Aspects of Computer Science, Saarbruecken, W. Ger., 3-5 Jan. 1985, Lecture Notes in Computer Science, Vol. 182, ed. K. Mehlhorn (Springer, New York, NY, 1985) 279-286.
39. B.K. Rosen, Linear cost is sometimes quadratic, in: Conf. Record of the Eighth ACM Symp. on Principles of Programming Languages, Williamsburg, VA, 26-28 January 1981 (ACM, New York, NY, 1981) 117-124.
40. B.G. Ryder and M.C. Paull, Incremental data flow analysis algorithms, ACM Trans. Program. Lang. Syst. 10(1) (1988) 1-50.
41. B.G. Ryder, W. Landi and H.D. Pande, Profiling an incremental data flow analysis algorithm, IEEE Trans. Software Eng. SE-16(2) (1990).
42. R. Sedgewick, Algorithms (Addison-Wesley, Reading, MA, 1983) 129-140.
43. P.M. Spira and A. Pan, On finding and updating spanning trees and shortest paths, SIAM J. Comput. 4(3) (1975) 375-380.
44. R.E. Tarjan, Data Structures and Network Algorithms (Society for Industrial and Applied Mathematics, Philadelphia, PA, 1983).
45. D. Yeh, On incremental evaluation of ordered attributed grammars, BIT 23 (1983) 308-320.
46. F.K. Zadeck, Incremental data flow analysis in a structured program editor, Proc. of the SIGPLAN 84 Symp. on Compiler Construction, Montreal, Can., 20-22 June 1984, ACM SIGPLAN Notices 19(6) (June 1984) 132-143.