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Stronger Linear Programming Relaxations of Max-Cut Computer Science, Mcgill University and GERAD
 

Summary: Stronger Linear Programming Relaxations of Max-Cut
David AVIS
Computer Science, Mcgill University and GERAD
3480 University, Montreal, Quebec, Canada H3A 2A7
avis@cs.mcgill.ca
Jun UMEMOTO
Graduate School of Informatics, Kyoto University
Yoshida-Honmachi, Sakyo-ku, Kyoto, Japan 606-8501
umemoto@kuis.kyoto-u.ac.jp
September 23, 2002
Abstract
We consider linear programming relaxations for the max cut problem in graphs, based on k-
gonal inequalities. We show that the integrality ratio for random dense graphs is asymptotically
1 + 1=k and for random sparse graphs is at least 1 + 3=k. There are O(n k ) k-gonal inequalities.
These results generalize work by Poljak and Tuza, who gave similar results for k = 3.
Resume
Nous considerons des relaxations lineaires serrees employant des contraintes k-gonales pour le
probleme de coupe maximale dans un graphe. Nous demontrons que pour des graphes aleatoires de
haute densite, le rapport d'integralite est asymptotiquement 1+1=k. Cependant, lorsqu'il s'agit de
graphes aleatoires de basse densite, ceci est au moins 1+3=k. Il existe O(nk) contraintes k-gonales.

  

Source: Avis, David - School of Computer Science, McGill University

 

Collections: Computer Technologies and Information Sciences