Local approximation of the Maximum Cut in regular graphs

Approximation Algorithm for Maximum Cut

Approximation Algorithms for the Maximum Cut Problem

Consider the problem of keeping closely related objects together and seperating unrelated objects from each other. This idea has clear applications to statistics, computer science, mathematics, social studies, and natural sciences just to name a few. To model this idea, we de ne the maximum cut problem that is simple to state but di cult to solve. The aim of this report is to provide two known ...

A conjecture on the maximum cut and bisection width in random regular graphs

The asymptotic properties of random regular graphs are objects of extensive study in mathematics and physics. In this paper we argue, using the theory of spin glasses in physics, that in random regular graphs the maximum cut size asymptotically equals the number of edges in the graph minus the minimum bisection size. Maximum cut and minimal bisection are two famous NP-complete problems with no ...

Conjecture on the maximum cut and bisection width in random regular graphs

Asymptotic properties of random regular graphs are object of extensive study in mathematics. In this note we argue, based on theory of spin glasses, that in random regular graphs the maximum cut size asymptotically equals the number of edges in the graph minus the minimum bisection size. Maximum cut and minimal bisection are two famous NP-complete problems with no known general relation between...

Combinatorial 5/6-approximation of Max Cut in graphs of maximum degree 3

The best approximation algorithm for Max Cut in graphs of maximum degree 3 uses semidefinite programming, has approximation ratio 0.9326, and its running time is Θ(n log n) ; but the best combinatorial algorithms have approximation ratio 4/5 only, achieved in O(n) time [Bondy and Locke, J. Graph Theory 10 (1986), 477–504 ; and Halperin et al., J. Algorithms 53 (2004), 169–185]. Here we present ...