Parameterized complexity and approximability of the SLCS problem

Authors:
S. Guillemot
Affiliations:
LIFL, CNRS, INRIA, Villeneuve d'Ascq cedex, France
Venue:
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Year:
2008

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Abstract

We introduce the Longest Compatible Sequence (Slcs)problem. This problem deals with p-sequences, which are strings on agiven alphabet where each letter occurs at most once. The Slcs problemtakes as input a collection of k p-sequences on a common alphabet Lof size n, and seeks a p-sequence on L which respects the precedenceconstraints induced by each input sequence, and is of maximal lengthwith this property.We investigate the parameterized complexity and theapproximability of the problem. As a by-product of our hardness resultsfor SLCS, we derive new hardness results for the Longest CommonSubsequence problem and other problems hard for the W-hierarchy.