Maximum dispersion problem in dense graphs

In this note, we present a polynomial-time approximation scheme for a ''dense case'' of dispersion problem in weighted graphs, where weights on edges are integers from {1,...,K} for some fixed integer K. The algorithm is based on the algorithmic version the regularity lemma.

[1]  S. S. Ravi,et al.  Heuristic and Special Case Algorithms for Dispersion Problems , 1994, Oper. Res..

[2]  Guy Kortsarz,et al.  On choosing a dense subgraph , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[3]  Uriel Feige,et al.  The Dense k -Subgraph Problem , 2001, Algorithmica.

[4]  Vojtech Rödl,et al.  The algorithmic aspects of the regularity lemma , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[5]  Vojtech Rödl,et al.  Constructive Quasi-Ramsey Numbers and Tournament Ranking , 1999, SIAM J. Discret. Math..

[6]  Marek Karpinski,et al.  Polynomial Time Approximation Schemes for Dense Instances of NP-Hard Problems , 1999, J. Comput. Syst. Sci..

[7]  Refael Hassin,et al.  Approximation algorithms for maximum dispersion , 1997, Oper. Res. Lett..

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

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

[10]  M. Simonovits,et al.  Szemeredi''s Regularity Lemma and its applications in graph theory , 1995 .