论文信息 - Constructive Quasi-Ramsey Numbers and Tournament Ranking

Constructive Quasi-Ramsey Numbers and Tournament Ranking

A constructive lower bound on the quasi-Ramsey numbers and the tournament ranking function was obtained in [S. Poljak, V. Rodl, and J. Spencer, SIAM J. Discrete Math., (1) 1988, pp. 372--376]. We consider the weighted versions of both problems. Our method yields a polynomial time heuristic with guaranteed lower bound for the linear ordering problem.

Vojtech Rödl | Andrzej Czygrinow | Svatopluk Poljak

[1] Jan Karel Lenstra,et al. Sequencing by enumerative methods , 1977 .

[2] Joel Spencer. Optimal ranking of tournaments , 1971, Networks.

[3] J. Spencer. Nonconstructive methods in discrete mathematics , 1978 .

[4] Alan M. Frieze,et al. Quick Approximation to Matrices and Applications , 1999, Comb..

[5] David P. Williamson,et al. .879-approximation algorithms for MAX CUT and MAX 2SAT , 1994, STOC '94.

[6] Wenceslas Fernandez de la Vega,et al. On the maximum cardinality of a consistent set of arcs in a random tournament , 1983, J. Comb. Theory, Ser. B.

[7] Vojtech Rödl,et al. The Algorithmic Aspects of the Regularity Lemma , 1994, J. Algorithms.

[8] Gerhard Reinelt,et al. A Cutting Plane Algorithm for the Linear Ordering Problem , 1984, Oper. Res..

[9] Vojtech Rödl,et al. A Fast Approximation Algorithm for Computing the Frequencies of Subgraphs in a Given Graph , 1995, SIAM J. Comput..

[10] Alan M. Frieze,et al. The regularity lemma and approximation schemes for dense problems , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[11] Vojtech Rödl,et al. Tournament Ranking with Expected Profit in Polynomial Time , 1988, SIAM J. Discret. Math..

[12] David S. Johnson,et al. Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[13] J. Spencer. Probabilistic Methods in Combinatorics , 1974 .

[14] E. Szemerédi. Regular Partitions of Graphs , 1975 .