Erratum to: The capacitated max k-cut problem

The Capacitated max-k-cut Problem

We consider a capacitated max k-cut problem in which a set of vertices is partitioned into k subsets. Each edge has a non-negative weight, and each subset has a possibly different capacity that imposes an upper bound on its size. The objective is to find a partition that maximizes the sum of edge weights across all pairs of vertices that lie in different subsets. We describe a local-search algo...

On the Budgeted Max-cut Problem and Its Application to the Capacitated Two-parallel Machine Scheduling

Maximum Cut Problem, MAX-CUT

The MAXIMUM CUT problem (MAX-CUT) is one of the simplest graph partitioning problems to conceptualize, and yet it is one of the most difficult combinatorial optimization problems to solve. The objective of MAX-CUT is to partition the set of vertices of a graph into two subsets, such that the sum of the weights of the edges having one endpoint in each of the subsets is maximum. This problem is k...

Max - cut Problem

Max-cut problem is one of many NP-hard graph theory problems which attracted many researchers over the years. Though there is almost no hope in finding a polynomialtime algorithm for max-cut problem, various heuristics, or combination of optimization and heuristic methods have been developed to solve this problem. Among them is the efficient algorithm of Goemans and Williamson. Their algorithm ...

The Capacitated K-Center Problem

The capacitated K-center problem is a fundamental facility location problem, where we are asked to locate K facilities in a graph, and to assign vertices to facilities, so as to minimize the maximum distance from a vertex to the facility to which it is assigned. Moreover, each facility may be assigned at most L vertices. This problem is known to be NP-hard. We give polynomial time approximation...