A network flow approach to the Minimum Common Integer Partition Problem

In the k-Minimum Common Integer Partition Problem, abbreviated as k-MCIP, 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.