Dynamic trees in practice

ACM Journal of Experimental Algorithmics

Volumn 14, Issue , 2009, Pages

  Tarjan, Robert E ^a   Werneck, Renato F ^b  

^a PRINCETON UNIVERSITY   (United States)

^b MICROSOFT RESEARCH   (United States)

Author keywords

Dynamic trees; Experimental evaluation; Link cut trees; Top trees

Indexed keywords

EID: 84862568306     PISSN: 10846654     EISSN: None     Source Type: Journal    
DOI: 10.1145/1498698.1594231     Document Type: Article

References (35)

1. ACAR, U. A., BLELLOCH, G. E., HARPER, R., VITTES, J. L., AND WOO, S. L. M. 2004. Dynamizing static algorithms, with applications to dynamic trees and history independence. In Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'04). SIAM, Philadelphia, 524-533.
2. ACAR, U. A., BLELLOCH, G. E., AND VITTES, J. L. 2005. An experimental analysis of change propagation in dynamic trees. In Proceedings of the 7th Workshop on Algorithm Engineering and Experiments (ALENEX'05). SIAM, Philadelphia, 41-54.
3. ADDARIO-BERRY, L., BROUTIN, N., AND REED, B. 2006. The diameter of the minimum spanning tree of a complete graph. In Proceedings of the 4th Colloquium on Mathematics and Computer Science. Discrete Mathematics and Theoretical Computer Science, Nancy, France, 237-248.
4. AHUJA, R., MAGNANTI, T., AND ORLIN, J. 1993. Network Flows: Theory, Algorithms, and Applications. Prentice-Hall, Upper Saddle River, NJ.
5. ALSTRUP, S., HOLM, J., DE LICHTENBERG, K., AND THORUP, M. 1997. Minimizing diameters of dynamic trees. In Proceedings of the 24th International Colloquium on Automata, Languages and Programming (ICALP'97). Springer, Berlin, 270-280.
6. ALSTRUP, S., HOLM, J., AND THORUP, M. 1999. On the power and speed of top trees. Unpublished manuscript.
7. ALSTRUP, S., HOLM, J., THORUP, M., AND DE LICHTENBERG, K. 2005. Maintaining information in fully dynamic trees with top trees. ACM Trans. Algorithms 1, 2, 243-264.
8. ANDERSON, R. 1993. The Washington graph generator. In DIMACS Series in Discrete Mathematics and Computer Science, D. S. Johnson and C. C. McGeoch, Eds. AMS, 580-581.
9. BELLMAN, R. 1958. BELLMAN, R. 1958. On a routing problem. Q. Math. 16, 87-90.
10. CATTANEO, G., FARUOLO, P., FERRARO-PETRILLO, U, AND ITALIANO, G. F. 2002. Maintaining dynamic minimum spanning trees: An experimental study. In Proceedings of the 4th Workshop on Algorithm Engineering and Experiments (ALENEX'02). Springer, Berlin, 111-125.
11. CHERKASSKY, B. V., GEORGIADIS, L., GOLDBERG, A. V., TARJAN, R. E., AND WERNECK, R. F. 2008. Shortest path feasibility algorithms: An experimental evaluation. In Proceedings of the 10th Workshop on Algorithm Engineering and Experiments (ALENEX'08). SIAM, Philadelphia, 118-132.
12. CHERKASSKY, B. V. AND GOLDBERG, A. V. 1999. Negative-cycle detection algorithms. Math. Program. 85, 277-311.
13. DINIC, E. A. 1970. Algorithm for solution of a problem of maximum flow in networks with power estimation. Soviet Mathematics Doklady 11, 1277-1280.
14. ACM Journal of Experimental Algorithmes, Vol. 14, Article No. 4.5, Publication date: September 2009.
15. EDMONDS, J. AND KARP, R. M. 1972. Theoretical improvements in algorithmic efficiency for network flow problems. J. ACM 19, 248-264.
16. FORD, JR., L. 1956. Network flow theory. Tech. rep. P-932, The Rand Corporation.
17. FREDERICKSON, G. N. 1985. Data structures for online update of minimum spanning trees, with applications. SIAM J. Comput. 14, 4, 781-798.
18. FREDERICKSON, G N. 1997a. Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees. SIAM J. Comput. 26, 2, 484-538.
19. FREDERICKSON, G. N. 1997b. A data structure for dynamically maintaining rooted trees. J. Algorithms 24, 1, 37-65.
20. GOLDBERG, A. V., GRIGORIADIS, M. D., AND TARJAN, R. E. 1991. Use of dynamic trees in a network simplex algorithm for the maximum flow problem. Math. Program. 50, 277-290.
21. HENZINGER, M. R. AND KING, V. 1997. Randomized fully dynamic graph algorithms with polylogarithmic time per operation. In Proceedings of the 29th Annual ACM Symposium on Theory of Computing (STOC'97). ACM, New York, 519-527.
22. KAPLAN, H., MOLAD, E., AND TARJAN, R. E. 2003. Dynamic rectangular intersection with priorities. In Proceedings of the 35th Annual ACM Symposium on Theory of Computing (STOC'03). ACM, New York, 639-648.
23. KLEIN, P. N. 2005. Multiple-source shortest paths in planar graphs. In Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'05). ACM, New York, 146-155.
24. LANGERMAN, S. 2000. On the shooter location problem: Maintaining dynamic circular-arc graphs. In Proceedings of the 12th Canadian Conference on Computational Geometry (CCCG'00). 29-35.
25. MILLER, G. L. AND REIF, J. H. 1985. Parallel tree contraction and its applications. In Proceedings of the 26th Annual IEEE Symposium on Foundations of Computer Science (FOCS'85). IEEE, Los Alamitos, CA, 478-489.
26. MOORE, E. F. 1959. The shortest path through a maze. In Proceedings of the International Symposium on the Theory of Switching. Harvard University Press, Cambridge, MA, 285-292.
27. RADZIK, T. 1998. Implementation of dynamic trees with in-subtree operations. ACM J. Exp. Algorithmes 3, 9.
28. RIBEIRO, C. C. AND TOSO, R. F. 2007. Experimental analysis of algorithms for updating minimum spanning trees on graphs subject to changes on edge weights. In Proceedings of the 6th Workshop on Experimental Algorithms (WEA'07). Springer, Berline, 393-405.
29. SLEATOR, D. D. AND TARJAN, R. E. 1983. A data structure for dynamic trees. J. Comput. Syst. Sci. 26, 3, 362-391.
30. SLEATOR, D. D. AND TARJAN, R. E. 1985. Self-adjusting binary search trees. J. ACM 32, 3, 652-686.
31. TARJAN, R. E. 1983. Data Structures and Network Algorithms. SIAM, Philadelphia.
32. TARJAN, R. E. 1997. Dynamic trees as search trees via Euler tours, applied to the network simplex algorithm. Math. Program. 78, 169-177.
33. TARJAN, R. E. AND WERNECK, R. F. 2005. Self-adjusting top trees. In Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'05). ACM, New York, 813-822.
34. WERNECK, R. F. 2006. Design and analysis of data structures for dynamic trees. Ph.D. thesis, Princeton University.
35. ZAROLIAGIS, C. D. 2002. Implementations and experimental studies of dynamic graph algorithms. In Experimental Algorithms: From Algorithm Design to Robust and Efficient Software, R. Fleischer, B. Moret, and E. M. Schmidt, Eds. Lecture Notes in Computer Science. Springer, Berlin, 229-278.