A network flow approach to the minimum common integer partition problem

Authors:
Wenbo Zhao;Peng Zhang;Tao Jiang
Affiliations:
Institute of Software, Chinese Academy of Sciences, Beijing, China and Graduate University of Chinese Academy of Sciences, Beijing, China;Institute of Software, Chinese Academy of Sciences, Beijing, China and Graduate University of Chinese Academy of Sciences, Beijing, China;Tsinghua University, Beijing, China and Department of Computer Science and Engineering, University of California at Riverside
Venue:
Theoretical Computer Science
Year:
2006

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Abstract

In the k-Minimum Common Integer Partition Problem, abbreviated as k-MCIE we are given k multisets X1,...,Xk of positive integers, the goal is to find an integer multiset T of the minimum size such that for every i, we can partition each of the integers in Xi so that the disjoint (multiset) union of their partitions equals T. This problem has applications in computational molecular biology, in particular, ortholog assignment and DNA hybridization fingerprint assembly. The problem is known to be NP-hard for any k ≥ 2. In this article, we improve the approximation ratio for k-MCIP by viewing this problem as a flow decomposition problem in some flow network. We show an efficient 0.5625k-approximation algorithm, improving upon the previously best known 0.6139k-approximation algorithm for this problem.