Parallel computations on strings and arrays

Abstract

We present several new parallel algorithms in the field of string and array processing. We give almost optimal algorithms for pattern matching in arrays and for related problem: longest common subarray, longest repeated subarray and longest symmetric subarray. We also give almost optimal algorithms for problems on strings: finding squares, testing even palstars, computing Lyndon factorizations and building pattern matching automata. In the PRAM model without concurrent writes, the parallel time is log(n)² with n processors and, in the PRAM model with concurrent writes, the time, for most of the problems, is log(n) with n processors. All the algorithms have in common the use of a parallel version of the Karp, Miller and Rosenberg's algorithm.

This work has been realized at the University of Paris-Nord.