Restricted and Swap Common Superstring: A Parameterized View

In several areas, in particular in bioinformatics and in AI planning, Shortest Common Superstring problem (SCS) and variants thereof have been successfully applied. In this paper we consider two variants of SCS recently introduced (Restricted Common Superstring, RCS) and (Swapped Common Superstring, SWCS). In RCS we are given a set S of strings and a multiset, and we look for an ordering Mo of M such that the number of input strings which are substrings of Mo is maximized. In SWCS we are given a set S of strings and a text T , and we look for a swap ordering To of T (an ordering of T obtained by swapping only some pairs of adjacent characters) such that the number of input strings which are substrings of To is maximized. In this paper we investigate the parameterized complexity of the two problems. We give two fixed-parameter algorithms, where the parameter is the size of the solution, for SWCS and -RCS (the RCS problem restricted to strings of length bounded by a parameter ). Furthermore, we complement these results by showing that SWCS and -RCS do not admit a polynomial kernel