The swap common superstring problem

Abstract

In this paper we consider an approach to solve the swap common superstring problem. This approach is based on an explicit reduction from the problem to the satisfiability problem.Keywords: swap common superstring, NP-complete, satisfiabilityThe algorithmic aspects of different problems of finding regularities are thoroughly studied in theoretical computer science (see e.g. [1] -[15]). In particular, the swap common superstring problem was proposed in [16].be a collection of strings over Σ. For simplicity, we use S[i] to denote the ith letter in string S, and S [i, j] to denote the substring of S consisting of the ith letter through the jth letter. The length of a string S is the number of letters in it and is denoted as |S|. Let 610 A. Gorbenko and V. PopovThe decision version of the swap common superstring problem can be formulated as following. The swap common superstring problem (SWCS):Instance: A collection S of strings over Σ, a string T , and a positive integer k.Question: Is there a string S such thatfor all 1 ≤ i < |S|, andThe problem SWCS is NP-hard [16]. Encoding different hard problems as instances of SAT and solving them with efficient satisfiability algorithms has caused considerable interest (see e.g. [17] -[36]). In this paper, we consider an approach to solve the SWCS problem. Our approach is based on an explicit reduction from the problem to the satisfiability problem.Let