Approximation algorithms for connected maximum cut and related problems

Approximation Algorithms for Connected Maximum Cut and Related Problems

An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V,E) and the goal is to find a subset of vertices S ⊆ V that maximizes the number of edges in the cut δ(S) such that the induced graph G[S] is connected. We present the first non-trivial Ω( 1 logn ) approximation algorithm for the Connected Maximum Cut problem in general graphs using novel techniques. We then ...

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 ...

Approximation algorithms for maximum cut with limited unbalance

We consider the problem of partitioning the vertices of a weighted graph into two sets of sizes that differ at most by a given threshold B, so as to maximize the weight of the crossing edges. For B equal to 0 this problem is known as Max Bisection, whereas for B equal to the number n of nodes it is the Maximum Cut problem. We present polynomial time randomized approximation algorithms with non ...

Approximation Algorithms for Feasible Cut and Multicut Problems

Let G = (V; E) be an undirected graph with a capacity function u : E!< + and let S 1 ; S 2 ; : : : ; S k be k commodities, where each S i consists of a pair of nodes. A set X of nodes is called feasible if it contains no S i , and a cut (X; X) is called feasible if X is feasible. Several optimization problems on feasible cuts are shown to be NP-hard. A 2-approximation algorithm for the minimum-...

Approximation Algorithm for Maximum Cut