Information Processing Letters 93 (2005) 307–313 www.elsevier.com/locate/ipl A Coarse-Grained Multicomputer algorithm for the detection of repetitions Thierry Garcia, David Semé ∗ LaRIA: Laboratoire de Recherche en Informatique d’Amiens, Université de Picardie Jules Verne, CURI, 5, rue du Moulin Neuf, 80000 Amiens, France Received 17 October 2003 Available online 11 January 2005 Communicated by F. Dehne Abstract The paper presents a Coarse-Grained Multicomputer algorithm that solves the problem of detection of repetitions. This algorithm can be implemented in the CGM model with P processors in O(N 2 /P ) in time and O(P ) communication steps. It is the first CGM algorithm for this problem. We present also experimental results showing that the CGM algorithm is very efficient.  2004 Elsevier B.V. All rights reserved. Keywords: Parallel algorithms; Coarse-Grained Multicomputers; Dynamic programming; String matching 1. Introduction This paper describes a Coarse-Grained Multicom- puter solution for the detection of repetitions. Strings of symbols containing no consecutive occurrences of the same pattern have attracted the attention of re- searchers in diverse fields for a long time. For exam- ple, repetitions play a crucial role in many domains [3,19] such as formal language theory, term rewriting, data compression and computational molecular biol- * Corresponding author. E-mail addresses: garcia@laria.u-picardie.fr (T. Garcia), seme@laria.u-picardie.fr (D. Semé). ogy. Perhaps their first appearance dates back to the work of Thue [23], who is generally credited with the discovery of arbitrary long streams of symbols from a finite alphabet that do not contain any “square” sub- strings, i.e., subpatterns formed by the concatenation of some substring with itself. In recent years, the study of such “square-free” strings has been found relevant to automata and for- mal language theory, algebraic coding and more gen- erally in systems theory and combinatorics, and we shall make no attempt to refer to the existing copious literature. Suffice it to mention that papers have been devoted to the construction of arbitrarily long square- free (as well as other related repetition-constrained) 0020-0190/$ – see front matter  2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ipl.2004.12.004