Dynamically switching vertices in planar graphs

Algorithmica (New York)

Volumn 28, Issue 1, 2000, Pages 76-103

  Frigioni, D ^a,b,c   Italiano, G F ^b,d  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

^c UNIVERSITY OF L'AQUILA   (Italy)

^d UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Connectivity; Dynamic algorithms; Planar graphs; Separators

Indexed keywords

EID: 0005369070     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004530010032     Document Type: Article

References (23)

1. D. Alberts, G. Cattaneo, G. F. Italiano. An empirical study of dynamic graph algorithms. ACM Journal on Experimental Algorithmics, 2 (1997), Article 5.
2. D. Alberts, M. R. Henzinger. Average case analysis of dynamic graph algorithms. Algorithmica, 20 (1998), 31-60.
3. G. Amato, G. Cattaneo, G. F. Italiano. Experimental analysis of dynamic minimum spanning tree algorithms. Proceedings of the 8th ACM-SIAM Symposium on Discrete Algorithms, 1997, pp. 314-323.
4. D. Eppstein, Z. Galil, G. F. Italiano, A. Nissenzweig. Sparsification - a technique for speeding up dynamic graph algorithms. Journal of the ACM, 44 (1997), 669-696.
5. D. Eppstein, Z. Galil, G. F. Italiano, T. H. Spencer. Separator based sparsification, I: planarity testing and minimum spanning trees. Journal of Computer and System Science, special issue of STOC '93, 52(1) (1996), 3-27.
6. D. Eppstein, Z. Galil, G. F. Italiano, T. H. Spencer. Separator based sparsification, II: edge and vertex connectivity. SIAM Journal on Computing, 28 (1999), 341-381.
7. D. Eppstein, G. F. Italiano, R. Tamassia, R. E. Tarjan, J. Westbrook, M. Yung. Maintenance of a minimum spanning forest in a dynamic plane graph. Journal of Algorithms, 13 (1992), 33-54.
8. G. N. Frederickson. Data structures for on-line updating of minimum spanning trees, with applications. SIAM Journal on Computing, 14 (1985), 781-798.
9. G. N. Frederickson. Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees. SIAM Journal on Computing, 26 (1997), 484-538.
10. D. Frigioni, A. Marchetti-Spaccamela, U. Nanni. Fully dynamic algorithms for maintaining shortest paths trees. Journal of Algorithms, 34 (2000), 251-281.
11. Z. Galil, G. F. Italiano, N. Sarnak. Fully dynamic planarity testing. Journal of the ACM, 46 (1999), 1-64.
12. M. T. Goodrich. Planar separators and parallel polygon triangulation. Journal of Computer and System Science, 51(3) (1995), 374-389.
13. M. R. Henzinger, V. King. Randomized dynamic graph algorithms with polylogarithmic time per operation. Proceedings of the 27th ACM Symposium on Theory of Computing, 1995, pp. 519-527.
14. M. R. Henzinger, V. King. Fully dynamic biconnectivity and transitive closure. Proceedings of the 36th IEEE Symposium on Foundations of Computer Science, 1995, pp. 664-672.
15. M. R. Henzinger, V. King. Maintaining minimum spanning trees in dynamic graphs. Proceedings of the 24th International Colloquium on Automata, Languages and Programming. LNCS 1256, Springer-Verlag, Berlin, 1997, pp. 594-604.
16. M. R. Henzinger, J. A. La Poutré. Certificates and fast algorithms for biconnectivity in fully dynamic graphs. Proceedings of the 3rd European Symposium on Algorithms. LNCS 979, Springer-Verlag, Berlin, 1995. pp. 171-184.
17. M. R. Henzinger, M. Thorup. Improved sampling with applications to dynamic algorithms. Proceedings of the 23rd International Colloquium on Automata, Languages and Programming. LNCS 1099, Springer-Verlag, Berlin, 1996, pp. 290-299.
18. J. Herschberger, M. Rauch, S. Suri. Fully dynamic 2-connectivity on planar graphs. Theoretical Computer Science, special issue on Dynamic and On-Line Algorithms, 130 (1994), 139-161.
19. J. Holm, K. de Lichtenberg, M. Thorup. Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge and biconnectivity. Proceedings of the 30th ACM Symposium on Theory of Computing, 1998, pp. 79-89.
20. R. J. Lipton, R. E. Tarjan. A separator theorem for planar graphs. SIAM Journal on Applied Mathematics, 36(1979), 177-189.
21. M. Rauch. Improved data structures for fully dynamic biconnectivity. Proceedings of the 26th ACM Symposium on Theory of Computing, 1994, pp. 686-695.
22. M. Rauch. Fully dynamic biconnectivity in graphs. Algorithmica, 13 (1995), 503-538.
23. M. Thorup. Decremental dynamic connectivity. Proceedings of the 8th ACM-SIAM Symposium on Discrete Algorithms, 1997, pp. 305-313.