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Projection results for the k-partition problem

Research output: Contribution to journalJournal article

E-pub ahead of print
<mark>Journal publication date</mark>6/09/2017
<mark>Journal</mark>Discrete Optimization
Number of pages15
<mark>State</mark>E-pub ahead of print
Early online date6/09/17
<mark>Original language</mark>English

Abstract

The k -partition problem is an NP -hard combinatorial optimisation problem with many applications. Chopra and Rao introduced two integer programming formulations of this problem, one having both node and edge variables, and the other having only edge variables. We show that, if we take the polytopes associated with the ‘edge-only’ formulation, and project them into a suitable subspace, we obtain the polytopes associated with the ‘node-and-edge’ formulation. This result enables us to derive new valid inequalities and separation algorithms, and also to shed new light on certain SDP relaxations. Computational results are also presented.

Bibliographic note

This is the author’s version of a work that was accepted for publication in Discrete Optimization. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Optimization, ??, ?, 2017 DOI: 10.1016/j.disopt.2017.08.001