An Improved Approximation Algorithm for the Minimum Common Integer Partition Problem

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8889)

Abstract

Given a collection of multisets \(\{X_1, X_2, \ldots , X_k\}\) (\(k \ge 2\)) of positive integers, a multiset \(S\) is a common integer partition for them if \(S\) is an integer partition of every multiset \(X_i, 1 \le i \le k\). The minimum common integer partition (\(k\)-MCIP) problem is defined as to find a CIP for \(\{X_1, X_2, \ldots , X_k\}\) with the minimum cardinality. We present a \(\frac{6}{5}\)-approximation algorithm for the \(2\)-MCIP problem, improving the previous best algorithm of ratio \(\frac{5}{4}\) designed in 2006. We then extend it to obtain an absolute \(0.6k\)-approximation algorithm for \(k\)-MCIP when \(k\) is even (when \(k\) is odd, the approximation ratio is \(0.6k+0.4\)).

Keywords

Stein Berman 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Computing ScienceUniversity of AlbertaEdmontonCanada

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