Weighted shortest common supersequence

Abstract

The Shortest Common Supersequence (SCS) is the problem of seeking a shortest possible sequence that contains each of the input sequences as a subsequence. In this paper we consider applying the problem to Position Weight Matrices (PWM). The Position Weight Matrix was introduced as a tool to handle a set of sequences that are not identical, yet, have many local similarities. Such a weighted sequence is a 'statistical image' of this set where we are given the probability of every symbol's occurrence at every text location. We consider two possible definitions of SCS on PWM. For the first, we give a polynomial time algorithm, having two input sequences. For the second, we prove NP-hardness. © 2011 Springer-Verlag.