On Maximal Repeats in Compressed Strings

Abstract

This paper presents and proves a new non-trivial upper bound on the number of maximal repeats of compressed strings. Using Theorem 1 of Raffinot\u27s article "On Maximal Repeats in Strings", this upper bound can be directly translated into an upper bound on the number of nodes in the Compacted Directed Acyclic Word Graphs of compressed strings. More formally, this paper proves that the number of maximal repeats in a string with z (self-referential) LZ77-factors and without q-th powers is at most 3q(z+1)^3-2. Also, this paper proves that for 2000 <= z <= q this upper bound is tight up to a constant factor