Better approximations for the minimum common integer partition problem

Authors:
David P. Woodruff
Affiliations:
MIT
Venue:
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Year:
2006

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Abstract

In the k-Minimum Common Integer Partition Problem, abbreviated k-MCIP, we are given k multisets X1, ..., Xk of positive integers, and the goal is to find an integer multiset T of minimal size for which for each i, we can partition each of the integers in Xi so that the disjoint union (multiset union) of their partitions equals T. This problem has many applications to computational molecular biology, including ortholog assignment and fingerprint assembly. We prove better approximation ratios for k-MCIP by looking at what we call the redundancy of X1, ..., Xk, which is a quantity capturing the frequency of integers across the different Xi. Namely, we show .614k-approximability, improving upon the previous best known (k – 1/3)-approximability for this problem. A key feature of our algorithm is that it can be implemented in almost linear time.