Abstract
We consider the longest common subsequence problem (lcs) and a variant of it where each symbol may occur at most once in the common subsequence. The lcs is a well-known problem that can be solved in polynomial time by a dynamic programming algorithm. We provide a complete description of a polytope we associate with the lcs. The integrality of this polytope can be derived by showing that it is in fact the clique polytope of a perfect graph. The repetition-free version of the problem is known to be difficult. We also associate a polytope with this version and investigate its facial structure. We present some valid and facet-defining inequalities for this polytope and discuss separation procedures. Finally, we present some computational results of a branch and cut algorithm we have implemented for this problem.
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Fernandes, C.G., Ferreira, C.E., Tjandraatmadja, C., Wakabayashi, Y. (2008). A Polyhedral Investigation of the LCS Problem and a Repetition-Free Variant. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds) LATIN 2008: Theoretical Informatics. LATIN 2008. Lecture Notes in Computer Science, vol 4957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78773-0_29
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DOI: https://doi.org/10.1007/978-3-540-78773-0_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78772-3
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