A local search algorithm for the constrained max cut problem on hypergraphs.
- Published
- Accepted
- Subject Areas
- Algorithms and Analysis of Algorithms, Optimization Theory and Computation
- Keywords
- Approximation Algorithms, Max k-cut problem, Local Search, Hypergraph
- Copyright
- © 2018 Samei et al.
- Licence
- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Preprints) and either DOI or URL of the article must be cited.
- Cite this article
- 2018. A local search algorithm for the constrained max cut problem on hypergraphs. PeerJ Preprints 6:e27434v1 https://doi.org/10.7287/peerj.preprints.27434v1
Abstract
In the constrained max k-cut problem on hypergraphs, we are given a weighted hypergraph H=(V, E), an integer k and a set c of constraints. The goal is to divide the set V of vertices into k disjoint partitions in such a way that the sum of the weights of the hyperedges having at least two endpoints in different partitions is maximized and the partitions satisfy all the constraints in c. In this paper we present a local search algorithm for the constrained max k-cut problem on hypergraphs and show that it has approximation ratio 1-1/k for a variety of constraints c, such as for the constraints defining the max Steiner k-cut problem, the max multiway cut problem and the max k-cut problem. We also show that our local search algorithm can be used on the max k-cut problem with given sizes of parts and on the capacitated max k-cut problem, and has approximation ratio 1-|Vmax|/|V|, where |Vmax| is the cardinality of the biggest partition. In addition, we present a local search algorithm for the directed max k-cut problem that has approximation ratio (k-1)/(3k-2).
Author Comment
This is a preprint submission to PeerJ Preprints.