Splay trees, Davenport-Schinzel sequences, and the deque conjecture

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2008, Pages 1115-1124

  Pettie, Seth ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DAVENPORT-SCHINZEL SEQUENCES; FUNCTION MAPPING; SPLAY TREES;

EID: 58449125496     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (34)

1. R. Adamec, M. Klazar, and P, Valtr, Generalized Davenport-Schinzel sequences with linear upper bound. Discrete Math., 108(1-3):219-229, 1992.
2. P. Agarwal, M. Shark, and P. Shor. Sharp upper and lower bounds on the length of general Davenport- Schinzel sequences. J. Combinatorial Theory, Series A, 52, 1989.
3. S. Albers. Improvd randomized on-line algorithms for the list update problem. SIAM J. Comput., 27(3):682-693, 1998.
4. S. Albers, B. von Stengel, and R. Werchner. A combined BIT and TIMESTAMP algorithm for the list update problem. Info. Proc. Lett., 56, 1995.
5. A. Blum, S. Chawla, and A. Kalai. Static optimality and dynamic search-optimality in lists and trees. Algorithmica, 36, 2003.
6. A. Buchsbaum, R. Sundar, and R. E. Tarjan. Datastructural bootstrapping, linear path compression, and catenable heap-ordered double-ended queues. SIAM J. Comput., 24, 1995.
7. R. Chaudhuri and H. Höft. Splaying a search tree in preorder takes linear time. International Journal of Mathematics and Mathematical Sciences, 13(1):186-186, 1990.
8. R. Cole. On the dynamic finger conjecture for splay trees. II. The proof. SIAM J. Comput., 30(1):44-85, 2000.
9. R. Cole, B. Mishra, J. Schmidt, and A. Siegel. On the dynamic finger conjecture for splay trees. I. Splay sorting log n-block sequences. SIAM J. Comput., 30(1):1-43, 2000.
10. E. Demaine, D. Harmon, J. Iacono, and M. Pǎtraşcu. Dynamic optimality - almost. In Proceedings 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 484-490, 2004.
11. A. Elmasry. On the sequential access theorem and deque conjecture for splay trees. Theoretical Computer Science, 314, 2004.
12. M. L. Fredman. On the efficiency of pairing heaps and related data structures. J. ACM, 46(4):473-501, 1999.
13. M. L. Fredman, R. Sedgewick, D. D. Sleator, and R. E. Tarjan. The pairing heap: a new form of selfadjusting heap. Algorithmica, 1(1):111-129, 1986.
14. G. F. Georgakopoulos. Splay trees: A reweighmg lemma and a proof of competitiveness vs. dynamic balanced trees. J. Algor., 51, 2004.
15. G. F. Georgakopoulos. How to splay for log log n- competitiveness. In Proc. 4th Int'l Workshop on Experimental and Efficient Algorithms, volume 3503, pages 570-579, 2005.
16. S. Hart and M. Sharir. Nonlinearity of Davenport- Schinzel sequences and of generalized path compression schemes. Combinatorica, 6(2):151-177, 1986.
17. Iacono. Key-independent optimality. Algorithmica, 42, 2005.
18. J. Iacono. Improved upper bounds for pairing heaps. In Scandinavian Workshop on Algorithm Theory (SWAT, LNCS 1851, pages 32-43, 2000.
19. John Iacono. Alternatives to splay trees with o(log n) worst-case access times. In SODA, pages 516-522, 2001.
20. M. Klazar. A general upper bound in extremal theory of sequences. Comment. Math. Univ. Carolin., 33(4):737-746, 1992.
21. M. Klazar, Generalized Davenport-Schinzel sequences: results, problems, and applications. Integers, 2:A11, 39 pp. (electronic), 2002.
22. M. Klazar and P. Valtr. Generalized Davenport- Schinzel sequences. Combinatorica, 14(4):463-476, 1994.
23. M. Loebl and J. Nešetřil. Linearity and unprovability of set union problem strategies. 1. Linearity of strong postorder. J. Algor., 23(2):207-220, 1997.
24. J. M. Lucas. Canonical forms for competitive binary search tree algorithms. Technical Report DCS-TR- 250, Rutgers University, 1988.
25. Joan M. Lucas. Postorder disjoint set union is linear. SIAM J. on Computing, 19(5):868-882, October 1990.
26. Joan M. Lucas. On the competitiveness of splay trees: Relations to the union-find problem. In Lyle A. McGeoch and Daniel D. Sleator, editors, On-line Algorithms, volume 7 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 95-124, 1991.
27. S. Pettie. Towards a final analysis of pairing heaps. In Proceedings 46th Annual Symposium on Foundations of Computer Science (FOCS), pages 174-183, 2005.
28. D. D. Sleator and R. E. Tarjan. Amortized efficiency of list update and paging rules. Comm. ACM, 28, 1985.
29. D. D. Sleator and R. E. Tarjan. Self-adjusting binary search trees. J. ACM, 32(3):652-686, 1985.
30. R. Sundar. On the deque conjecture for the splay algorithm. Combinatorica, 12(1):95-124, 1992.
31. R. E. Tarjan. Efficiency of a good but not linear set merging algorithm. J. ACM, 22:215-225, 1975.
32. R.E. Tarjan. Sequential access in play trees takes linear time. Combinatorica, 5(4):367-378, 1985.
33. C. Wang, J. Derryberry, and D. Sleator. O(log log n)-competitive dynamic binary search trees. In Proc. 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2006.
34. R. Wilber. Lower bounds for accessing binary search trees with rotations. SIAM J. Comput., 18(1):56-67, 1989.