An inverse-Ackermann style lower bound for the online minimum spanning tree verification problem

Annual Symposium on Foundations of Computer Science - Proceedings

Volumn , Issue , 2002, Pages 155-163

  Pettie, Seth ^a  

^a University of Texas at Austin   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; DECISION THEORY; INVERSE PROBLEMS; MATHEMATICAL MODELS; MATRIX ALGEBRA; ONLINE SYSTEMS; PROBLEM SOLVING;

LINEAR PREPROCESSING TIME; MINIMUM SPANNING TREE VERIFICATION PROBLEM;

DATA STRUCTURES;

EID: 0036956948     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (39)

1. W. Ackermann. Zum Hilbertshen aufbau der reelen zahlen. Math. Ann., 99:118-133, 1928.
2. A. Alon and B. Schieber. Optimal preprocessing for answering on-line product queries. Technical Report TR-71/87, Institute of Computer Science, Tel Aviv University, 1987.
3. A. Bar-Noy, R. Motwani, and J. Naor. A linear time approach to the set maxima problem. SIAM J. Discr. Math., 5(1):1-9, 1992.
4. H. Brönnimann, B. Chazelle, and J. Pach. How hard is half-space range searching? Discrete Comput. Geom., 10(2):143-155, 1993.
5. A. L. Buchsbaum, H. Kaplan, A. Rogers, and J. R. Westbrook. Linear-time pointer-machine algorithms for LCAs, MST verification, and dominators. In Proc. 30th ACM Symposium on Theory of Computing (STOC'98), pages 279-288, May 23-26 1998.
6. B. Chazelle. Computing on a free tree via complexity-preserving mappings. Algorithmica, 2(3):337-361, 1987.
7. B. Chazelle. Lower bounds on the complexity of polytope range searching. J. Amer. Math. Soc., 2(4):637-666, 1989.
8. B. Chazelle. Lower bounds for orthogonal range searching: II. the arithmetic model. J. ACM, 37(3):439-463, July 1990.
9. B. Chazelle. Lower bounds for off-line range searching. Discrete Comput. Geom., 17(1):53-65, 1997.
10. B. Chazelle. A minimum spanning tree slgorithm with inverse-Ackermann type complexity. J. ACM, 47(6):1028-1047, 2000.
11. B. Chazelle. The soft heap: an approximate priority queue with optimal error rate. J. ACM, 47(6):1012-1027, 2000.
12. B. Chazelle and B. Rosenberg. Computing partial sums in multidimensional arrays. In Proc. 5th Annual Symposium on Computational Geometry (SCG'89), pages 131-139, 1989.
13. B. Chazelle and B. Rosenberg. The complexity of computing partial sums off-line. Internat. J. Comput. Geom. Appl., 1(1):33-45, 1991.
14. B. Chazelle and B. Rosenberg. Simplex range reporting on a pointer machine. Comput. Geom., 5(5):237-247, 1996.
15. T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press, Cambridge, Mass., 1990.
16. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. Introduction to Algorithms. MIT Press, 2001.
17. B. Dixon, M. Rauch, and R. E. Tarjan. Verification and sensitivity analysis of minimum spanning trees in linear time. SIAM J. Comput., 21(6):1184-1192, 1992.
18. M. L. Fredman. A lower bound on the complexity of orthogonal range queries. J. ACM, 28(4):696-705, 1981.
19. H. N. Gabow. A scaling algorithm for weighted matching on general graphs. In Proc. 26th Annual Symposium on Foundations of Computer Science (FOCS'85), pages 90-100, 1985.
20. W. Goddard, C. Kenyon, V. King, and L. Schulman. Optimal randomized algorithms for local sorting and set-maxima. SIAM J. Comput., 22(2):272-283, 1993.
21. T. Hagerup. Improved shortest paths on the word RAM. In Proc. 27th Int'l Colloq. on Automata, Languages, and Programming (ICALP'00), LNCS vol. 1853, pages 61-72, 2000.
22. S. Hart and M. Sharir. Nonlinearity of Davenport-Schinzel sequences and of generalized path compression schemes. Combinatorica, 6(2):151-177, 1986.
23. D. Karger, P. N. Klein, and R. E. Tarjan. A randomized linear-time algorithm for finding minimum spanning trees. J. ACM, 42:321-329, 1995.
24. V. King. A simpler minimum spanning tree verification algorithm. Algorithmica, 18(2):263-270, 1997.
25. M. M. Klawe. Superlinear bounds on matrix searching. In D. Johnson, editor, Proc. 1st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'90), pages 485-493, 1990.
26. M. M. Klawe and D. J. Kleitman. An almost linear time algorithm for generalized matrix searching. SIAM J. Discr. Math., 3(1):81-97, Feb. 1990.
27. J. Komlós. Linear verification for spanning trees. Combinatorica, 5(1):57-65, 1985.
28. H. LaPoutré. Lower bounds for the union-find and the split-find problem on pointer machines. J. Comput. Syst. Sci., 52:87-99, 1996.
29. S. Pettie. A faster all-pairs shortest path algorithm for real-weighted sparse graphs. In Proc. 29th Int'l Colloq. on Automata, Languages, and Programming (ICALP'02), LNCS vol. 2380, pages 85-97, 2002.
30. S. Pettie. On the comparison-addition complexity of all-pairs shortest paths. In Proc. 13th Int'l Symp. on Algorithms and Computation (ISAAC'02), pages ??-??, 2002.
31. S. Pettie and V. Ramachandran. Computing shortest paths with comparisons and additions. In Proc. 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'02), pages 267-276, 2002.
32. S. Pettie and V. Ramachandran. Minimizing randomness in minimum spanning tree, parallel connectivity and set maxima algorithms. In Proc. 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'02), pages 713-722, 2002.
33. S. Pettie and V. Ramachandran. An optimal minimum spanning tree algorithm. J. ACM, 49(1):16-34, 2002.
34. R. E. Tarjan. Applications of path compression on balanced trees. J. ACM, 26(4):690-715, 1979.
35. R. E. Tarjan. A class of algorithms which require nonlinear time to maintain disjoint sets. J. Comput. Syst. Sci., 18(2):110-127, 1979.
36. R. E. Tarjan. Sensitivity analysis of minimum spanning trees and shortest path problems (see also corrigendum IPL 23(4), p. 219). Info. Proc. Lett., 14(1):30-33, 1982.
37. M. Thorup. Undirected single-source shortest paths with positive integer weights in linear time. J. ACM, 46(3):362-394, 1999.
38. A. C. Yao Space-time tradeoff for answering range queries. In Proc. 14th ACM Symposium on Theory of Computing (STOC'82), pages 128-136, 1982.
39. A. C. Yao. On the complexity of maintaining partial sums. SIAM J. Comput., 14(2):277-288, 1985.