Trees, stars, and multiple biological sequence alignment
SIAM Journal on Applied Mathematics
SIAM Journal on Discrete Mathematics
Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
On Local Search for Weighted K-Set Packing
Mathematics of Operations Research
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Introduction to Algorithms
Assignment of Orthologous Genes via Genome Rearrangement
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Approximating reversal distance for strings with bounded number of duplicates
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Minimum common string partition problem: hardness and approximations
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
A network flow approach to the minimum common integer partition problem
Theoretical Computer Science
Minimum Common String Partition Parameterized
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
Better approximations for the minimum common integer partition problem
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
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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 S1, ⋯, Sk of integers, where k ≥ 2, we say that a multiset is a common integer partition if it is an integer partition of every multiset Si, 1≤ i≤ k. The MCIP problem is thus defined as to find a common integer partition of S1, ⋯, Sk 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.