Average-case analysis of dynamic graph algorithms

Algorithmica (New York)

Volumn 20, Issue 1, 1998, Pages 31-60

  Alberts, D ^a   Henzinger, M R ^b  

^a MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

^b HEWLETT PACKARD COMPANY   (United States)

Author keywords

Average case analysis; Bipartiteness; Connectivity; Dynamic graph algorithm; Maximum matching; Minimum spanning forest

Indexed keywords

EID: 4243147705     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00009186     Document Type: Article

References (35)

1. D. Alberts and M. R. Henzinger. Average case analysis of dynamic graph algorithms. In Proc. 6th Symp. on Discrete Algorithms, pages 312-321, 1995.
2. H. Alt, K. Mehlhorn, H. Wagener, and E. Welzl. Congruence, similarity, and symmetries of geometric objects. Discrete Comput. Geom., 3:237-256, 1988.
3. B. Bollobás. Random Graphs. Academic Press, London, 1985.
4. J. Cheriyan, M. Y. Kao, and R. Thurimella. Algorithms for parallel k-vertex connectivity and sparse certificates. SIAM J. Comput., 22:157-174, 1993.
5. L. P. Chew. Building voronoi diagrams for convex polygons in linear expected time. CS Tech Report TR90-147, Dartmouth College, Hanover, NH, 1986.
6. K. L. Clarkson, K. Mehlhorn, and R. Seidel. Four results on randomized incremental constructions. Comput. Geom. Theory Appl., 3:185-212, 1993.
7. J. Edmonds. Paths, trees, and flowers. Canad. J. Math., 17:449-467, 1965.
8. D. Eppstein. Average case analysis of dynamic geometric optimization. In Proc. 5th Symp. on Discrete Algorithms, pages 77-86, 1994.
9. D. Eppstein. Personal communication, 1995.
10. D. Eppstein, Z. Galil, and G. F. Italiano. Improved sparsification. Technical Report 93-20, Dept. of Information and Computer Science, University of California, Irvine, CA, 1993.
11. D. Eppstein, Z. Galil, G. F. Italiano, and A. Nissenzweig. Sparsification - a technique for speeding up dynamic graph algorithms. In Proc. 33rd Symp. on Foundations of Computer Science, pages 60-69, 1992.
12. G. N. Frederickson. Data structures for on-line updating of minimum spanning trees, with applications. SIAM J. Comput., 14:781-798, 1985.
13. G. N. Frederickson. Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees. In Proc. 32nd Symp. on Foundations of Computer Science, pages 632-641, 1991.
14. H. N. Gabow. Implementation of algorithms for maximum matching on nonbipartite graphs. Ph.D. thesis, Dept. of Computer Science, Stanford University, Stanford, CA, 1973.
15. H. N. Gabow. A matroid approach to finding edge connectivity and packing arborescences. In Proc. 23rd Symp. on Theory of Computing, pages 112-122, 1991.
16. Z. Galil. Finding the vertex connectivity of graphs. SIAM J. Comput., 9:197-199, 1980.
17. M. R. Henzinger. Fully dynamic cycle equivalence in graphs. In Proc. 35th Symp. on Foundations of Computer Science, pages 744-755, 1994.
18. M. R. Henzinger and V. King. Randomized dynamic algorithms with polylogarithmic time per operation. In Proc. 27th Symp. on Theory of Computing, pages 519-527, 1995.
19. M. R. Henzinger and M. Thorup. Improved sampling with applications to dynamic graph algorithms. In Proc. ICALP '96, pages 290-299, 1996.
20. R. M. Karp. Personal communications.
21. P. N. Klein and R. E. Tarjan. A linear-time algorithm for the minimum spanning tree. In Proc. 26th Symp. on Theory of Computing, pages 9-15, 1994.
22. P. M. Lewis, R. E. Stearns, and J. Hartmanis. Memory bounds for recognition of context-free and context-sensitve languages. In Proc. IEEE Conf. on Switching Theory and Logical Design, pages 191-202, 1965.
23. L. Lovász and M. D. Plummer. Matching Theory. Annals of Discrete Mathematics, volume 29. North-Holland, Amsterdam, 1986.
24. 1/2E) algorithm for finding maximum matching in general graphs. In Proc. 21st Symp. on Foundations of Computer Science, pages 17-27, 1980.
25. K. Mulmuley. Randomized, multidimensional search trees: dynamic sampling. In Proc. 7th Symp. on Computational Geometry, pages 121-131, 1991.
26. H. Nagamochi and T. Ibaraki. Lineartime algorithms for finding a sparse k-connected spanning subgraph of a k-connected graph. Algorithmica, 7:583-596, 1992.
27. M. H. Rauch. Fully dynamic biconnectivity in graphs. In Proc. 33rd Symp. on Foundations of Computer Science, pages 50-59, 1992.
28. M. H. Rauch. Improved data structures for fully dynamic biconnectivity. In Proc. 26th Symp. on Theory of Computing, pages 686-695, 1994.
29. J. H. Reif, P. G. Spirakis, and M. Yung. Re-randomization and average case analysis of fully dynamic graph algorithms. Alcom Technical Report TR 93.01.3.
30. O. Schwarzkopf. Dynamic maintenance of convex polytopes and related structures. Ph.D. thesis, Freie Universität Berlin, Berlin, 1992.
31. R. Seidel. Backwards analysis of randomized geometric algorithms. In J. Pach, editor, New Trends in Discrete and Computational Geometry, pages 37-67. Springer-Verlag, Berlin, 1993.
32. D. D. Sleator and R. E. Tarjan. A data structure for dynamic trees. J. Comput. System Sci., 26:362-391, 1983.
33. R. E. Tarjan. Data Structures and Network Algorithms. CBMS-NSF Regional Conference Series in Applied Mathematics, volume 44. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1983.
34. R. Thurimella. Techniques for the design of parallel graph algorithms. Ph.D. thesis, University of Texas, Austin, TX, 1989.
35. V. V. Vazirani. A theory of alternating paths and blossoms for proving correctness of the O(√V E) general graph maximum matching algorithm. Combinatorica, 14(1):71-109, 1994.