On the parallel dynamic dictionary matching problem: New results with applications

Abstract

In the Parallel Dynamic Dictionary Matching (DDM) problem, a dictionary:D contains a set of patterns that can change over time under insertion and deletion of individual patterns. D has to be properly maintained such that, given an arbitrary text T, for each position in T we have to list in parallel the longest pattern of D occurring there. In this paper, we follow a completely new approach thus providing the first parallel algorithm for the DDM problem which achieves optimal (amortized) work for the update operations in the case of both a constant sized and an unbounded alphabet. It requires small "space and still preserves the same time and work of the best known CRCW-PRAM algorithm [27] for answering queries on an arbitrary text. Furthermore, our parallel approach gives new useful insights for the sequential solution of the DDM problem both in main memory and in secondary storage, and either on strings or on parameterized strings [7].