A local search algorithm for the constrained max cut problem on hypergraphs.
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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).
Cite this as
2018. A local search algorithm for the constrained max cut problem on hypergraphs. PeerJ Preprints 6:e27434v1 https://doi.org/10.7287/peerj.preprints.27434v1Author comment
This is a preprint submission to PeerJ Preprints.
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Competing Interests
The authors declare that they have no competing interests.
Author Contributions
Nasim Samei conceived and designed the experiments, analyzed the data, prepared figures and/or tables, authored or reviewed drafts of the paper.
Roberto Solis-Oba conceived and designed the experiments, authored or reviewed drafts of the paper, approved the final draft.
Data Deposition
The following information was supplied regarding data availability:
We haven't done any experiment in our article. Our article include analyzing the local search algorithm for the constrained max cut problem theoretically.
Funding
The research of the second author, professor Roberto Solis-Oba, was partially supported by the Natural Sciences and Engineering Research Council of Canada, grant 04667-2015 RGPIN. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
