Abstract

We introduce the Longest Compatible Sequence ( Slcs ) problem. This problem deals with p-sequences, which are strings on a given alphabet where each letter occurs at most once. The Slcs problem takes as input a collection of k p -sequences on a common alphabet L of size n , and seeks a p -sequence on L which respects the precedence constraints induced by each input sequence, and is of maximal length with this property. We investigate the parameterized complexity and the approximability of the problem. As a by-product of our hardness results for the Slcs problem, we derive new hardness results for the Longest Common Subsequence problem and other problems that are hard for the W -hierarchy.

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