An Improved Approximation Algorithm for MULTIWAY CUT

An improved approximation algorithm for requirement cut

This note presents improved approximation guarantees for the requirement cut problem: given an n-vertex edge-weighted graph G = (V , E), and g groups of vertices X1, . . . , Xg ⊆ V with each group Xi having a requirement ri between 0 and |Xi|, the goal is to find aminimum cost set of edges whose removal separates each group Xi into at least ri disconnected components. We give a tightΘ(log g) ap...

Improved Approximation Algorithm for Requirement Cut

This note presents improved approximation guarantees for the requirement cut problem: given an n-vertex edge-weighted graph G = (V,E), g groups of vertices X1, · · · , Xg ⊆ V with each group Xi having a requirement ri between 0 and |Xi|, the goal is to find a minimum cost set of edges whose removal separates each group Xi into at least ri disconnected components. We give a tight Θ(log g) approx...

An Efficient Approximation Algorithm for Max-Cut

Significant research effort has been devoted in the study of approximation algorithms for NP-hard problems. Ap-proximation algorithm for Max-Cut problem with performance guarantee of 0. 87856 is long known. In this work we study balanced Max-Cut problem. We give a balancing factor ? for given ? such that the approximate solution is at least 0. 87856 times the optimal ?-balanced cut and it is it...

A polynomial-time approximation scheme for planar multiway cut

Given an undirected graph with edge lengths and a subset of nodes (called the terminals), a multiway cut (also called a multi-terminal cut) problem asks for a subset of edges with minimum total length and whose removal disconnects each terminal from the others. It generalizes the min st-cut problem but is NP-hard for planar graphs and APX-hard for general graphs. We give a polynomial-time appro...

Approximation Algorithm for Maximum Cut