Improved bounds and new techniques for Davenport-Schinzel sequences and their generalizations

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2009, Pages 1-10

  Nivasch, Gabriel ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS;

A-COEFFICIENT; DAVENPORT-SCHINZEL SEQUENCES; INVERSE ACKERMANN FUNCTION; LOWER BOUNDS; LOWER ORDER TERMS; NEW RESULTS; UPPER BOUND;

INVERSE PROBLEMS;

EID: 70349111826     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973068.1     Document Type: Conference Paper

References (17)

1. R. Adamec, M. Klazar, and P. Valtr, Generalized Davenport-Schinzel sequences with linear upper bound, Discrete Math., 108:219-229, 1992.
2. P. K. Agarwal, M. Sharir, and P. Shor, Sharp upper and lower bounds for the length of general Davenport-Schinzel sequences, J. Comb. Theory, Ser. A, 52:228-274, 1989.
3. N. Alon and E. Friedgut, On the number of permutations avoiding a given pattern, J. Comb. Theory, Ser. A, 89:133-140, 2000.
4. N. Alon, H. Kaplan, G. Nivasch, M. Sharir, and S. Smorodinsky, Weak ε-nets and interval chains, to appear in J. ACM. Available at http://www.cs.tau.ac.il/research/gabriel.nivasch/publications/papers/ interval-chains.pdf.
5. H. Davenport and A. Schinzel, A combinatorial problem connected with differential equations, American J. Math., 87:684-694, 1965.
6. S. Hart and M. Sharir, Nonlinearity of Davenport-Schinzel sequences and of generalized path compression schemes, Combinatorica, 6:151-177, 1986.
7. M. Klazar, A general upper bound in extremal theory of sequences, Comment. Math. Univ. Carol., 33:737-746, 1992.
8. M. Klazar, On the maximum lengths of Davenport-Schinzel sequences, in R. Graham et al., editors, Contemporary Trends in Discrete Mathematics (DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 49), pp. 169-178, Amer. Math. Soc., Providence, RI, 1999.
9. M. Klazar, Generalized Davenport-Schinzel sequences: Results, problems, and applications, Integers, 2:A11, 39 pp. (electronic), 2002.
10. P. Komjáth, A simplified construction of nonlinear Davenport-Schinzel sequences, J. Comb. Theory, Ser. A, 49:262-267, 1988.
11. A. Marcus and G. Tardos, Excluded permutation matrices and the Stanley-Wilf conjecture, J. Comb. Theory, Ser. A, 107:153-160, 2004.
12. S. Pettie, Splay trees, Davenport-Schinzel sequences, and the deque conjecture, in Proc. 19th Annu. ACM-SIAM Sympos. Discrete Algorithms (SODA), 1115-1124, 2008.
13. R. Seidel, Understanding the inverse Ackermann function, PDF presentation. Available at http://cgi.di.uoa.gr/~ewcg06/invited/Seidel.pdf.
14. M. Sharir and P. K. Agarwal, Davenport-Schinzel Sequences and Their Geometric Applications, Cambridge University Press, Cambridge, 1995.
15. R. Sundar, On the deque conjecture for the splay algorithm, Combinatorica, 12:95-124, 1992.
16. P. Valtr, Generalizations of Davenport-Schinzel sequences, in R. Graham et al., editors, Contemporary Trends in Discrete Mathematics (DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 49), pp. 349-389, Amer. Math. Soc., Providence, RI, 1999.
17. A. Wiernik and M. Sharir, Planar realizations of nonlinear Davenport-Schinzel sequences by segments, Discrete Comput. Geom., 3:15-47, 1988.