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An Improved Approximation Algorithm for the Minimum Common Integer Partition Problem

  • Weitian Tong
  • Guohui Lin
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

Approximation Algorithm Bipartite Graph Approximation Ratio Performance Ratio Minimum Cardinality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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