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- W1837621982 abstract "We introduce a new combinatorial optimization problem in this paper, called the Minimum Common Integer Partition (MCIP) problem, which was inspired by computational biology applications including ortholog assignment and DNA fingerprint assembly. A partition of a positive integer n is a multiset of positive integers that add up to exactly n, and an integer partition of a multiset S of integers is defined as the multiset union of partitions of integers in S. Given a sequence of multisets S 1, ⋯, S k of integers, where k ≥ 2, we say that a multiset is a common integer partition if it is an integer partition of every multiset S i , 1≤ i≤ k. The MCIP problem is thus defined as to find a common integer partition of S 1, ⋯, S k with the minimum cardinality. It is easy to see that the MCIP problem is NP-hard since it generalizes the well-known Set Partition problem. We can in fact show that it is APX-hard. We will also present a $frac{5}{4}$ -approximation algorithm for the MCIP problem when k = 2, and a $frac{3k(k-1)}{3k-2}$ -approximation algorithm for k ≥ 3." @default.
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- W1837621982 date "2006-01-01" @default.
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- W1837621982 title "On the Minimum Common Integer Partition Problem" @default.
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- W1837621982 doi "https://doi.org/10.1007/11758471_24" @default.
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