Time-Space Trade-Offs for the Longest Common Substring Problem

Abstract

The Longest Common Substring problem is to compute the longest substring which occurs in at least d ≥ 2 of m strings of total length n. In this paper we ask the question whether this problem allows a deterministic time-space trade-off using O(n ^1 + ε) time and O(n ^1 − ε) space for 0 ≤ ε ≤ 1. We give a positive answer in the case of two strings (d = m = 2) and 0 < ε ≤ 1/3. In the general case where 2 ≤ d ≤ m, we show that the problem can be solved in O(n ^1 − ε) space and O( n ^1 + εlog² n (d log² n + d ²)) time for any 0 ≤ ε < 1/3.