Restricted common superstrings

Abstract

In this paper we consider an approach to solve the restricted common superstring problem. This approach is based on an explicit reduction from the problem to the satisfiability problem.Keywords: restricted common superstring, NP-complete, satisfiabilityComputational complexity of different problems of finding regularities and efficient algorithms for these problems are thoroughly studied in theoretical computer science (see e.g. [1] -[6]). In particular, complexity of the restricted common superstring problem and some approximation algorithms for the problem was considered in [7,8].Let Σ = {a 1 , . . . , a m } be a finite alphabet. Let S = {S 1 , . . . , S n } be a set of strings over Σ. We assume that S[i] is the ith letter in string S. Also, we assume that S [i, j] is 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. We assume that |S| is the length of S. We use #occ(X, Y ) to denote |{i | X = Y [i, j]}|.

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