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. © 2014 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Boria, N., Kurpisz, A., Leppänen, S., & Mastrolilli, M. (2014). Improved approximation for the maximum duo-preservation string mapping problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8701 LNBI, pp. 14–25). Springer Verlag. https://doi.org/10.1007/978-3-662-44753-6_2
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