Abstract
In this paper we present improved approximation results for the max duo-preservation string mapping problem (MPSM) introduced in [Chen et al., Theoretical Computer Science, 2014] that is complementary to the well-studied min common string partition problem (MCSP). When each letter occurs at most k times in each string the problem is denoted by k-MPSM. First, we prove that k-MPSM is APX-Hard even when k = 2. Then, we improve on the previous results by devising two distinct algorithms: the first ensures approximation ratio 8/5 for k = 2 and ratio 3 for k = 3, while the second guarantees approximation ratio 4 for any bigger value of k. Finally, we address the approximation of constrained maximum induced subgraph (CMIS, a generalization of MPSM, also introduced in [Chen et al., Theoretical Computer Science, 2014]), and improve the best known 9-approximation for 3-CMIS to a 6-approximation, by using a configuration LP to get a better linear relaxation. We also prove that such a linear program has an integrality gap of k, which suggests that no constant approximation (i.e. independent of k) can be achieved through rounding techniques.
Research supported by the Swiss National Science Foundation project \(200020\_ 144491\slash 1\) “Approximation Algorithms for Machine Scheduling Through Theory and Experiments”, and by the Sciex-Project 12.311
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Boria, N., Kurpisz, A., Leppänen, S., Mastrolilli, M. (2014). Improved Approximation for the Maximum Duo-Preservation String Mapping Problem. In: Brown, D., Morgenstern, B. (eds) Algorithms in Bioinformatics. WABI 2014. Lecture Notes in Computer Science(), vol 8701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44753-6_2
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DOI: https://doi.org/10.1007/978-3-662-44753-6_2
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