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SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
More efficient algorithms for closest string and substring problems
RECOMB'08 Proceedings of the 12th annual international conference on Research in computational molecular biology
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COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
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Computers and Operations Research
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Computers and Operations Research
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SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
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In this paper we study the closest-string problem (CSP), which can be defined as follows: Given a finite set = {s1, s2, ', sn} of strings, each string with length m, find a center string t of length m minimizing d, such that for every string si â聢聢 , dH(t, si) â聣陇 d. By dH(t, si) we mean the Hamming distance between t and si. This is an NP-hard problem, with applications in molecular biology and coding theory. Even though there are good approximation algorithms for this problem, and exact algorithms for instances with d constant, there are no studies trying to solve it exactly for the general case. In this paper we propose three integer-programming (IP) formulations and a heuristic, which is used to provide upper bounds on the value of an optimal solution. We report computational results of a branch-and-bound algorithm based on one of the IP formulations, and of the heuristic, executed over randomly generated instances. These results show that it is possible to solve CSP instances of moderate size to optimality.