Improved length bounds for the shortest superstring problem

Abstract

Given a collection of strings S={s ₁,...,s _n } over an alphabet Σ, a superstring α of S is a string containing each s _i as a substring; that is, for each i, 1 ≤ i ≤ n, α contains a block of ¦s _i¦ consecutive characters that match s _i exactly. The shortest superstring problem is the problem of finding a superstring α of minimum length. This problem is NP-hard [6] and has applications in computational biology and data compression. The first O(1)-approximation algorithms were given in [2]. We describe our 2 3/4-approximation algorithm, which is the best known. While our algorithm is not complex, our analysis requires some novel machinery to describe overlapping periodic strings. We then show how to combine our result with that of [11] to obtain a ratio of 2 50/69 ≈ 2.725. We describe an implementation of our algorithm which runs in O(¦S¦+n ³) time; this matches the running time of previous O(1)-approximations.

This work was done while the author was at Dartmouth College.

Research partly supported by NSF Award CCR-9308701, a Walter Burke Research Initiation Award and a Dartmouth College Research Initiation Award.