On the approximation of finding various minimal, maximal, and consistent sequences

Abstract

In this paper we investigate the complexity of finding various kinds of common super-and subsequences with respect to one or two given sets of strings. We show how these problems can be related to finding sequences having a fixed character composition. This leads to a unified approach for characterizing the complexity of such problems. Moreover, we derive interesting results on the approximability of problems which are dual to the well known Shortest Common Supersequence and Longest Common Subsequence problems.