Some approximations for shortest common nonsubsequences and supersequences

Abstract

This paper is devoted to polynomial-time approximations for the problems of finding a shortest common nonsubsequence and a shortest common supersequence of given strings. The main attention is paid to the special case of the latter problem where all given strings are of length two. We show strong connections of this case to the feedback vertex set problem, the maximal network flow problem and the maximal multi-commodity network flow problem.