Optimal speedups for parallel pattern matching in trees

Abstract

Tree pattern matching is a fundamental operation that is used in a number of programming tasks such as code optimization in compilers, symbolic computation, automatic theorem proving and term rewriting. An important special case of this operation is linear tree pattern matching in which an instance of any variable in the pattern occurs at most once. If n and m are the number of nodes in the subject and pattern tree respectively and if no restriction is placed on the structure of the trees, then the fastest known sequential algorithm for linear tree pattern matching requires O(nm) time in the worst case. In this paper we present a parallel algorithm for linear tree pattern matching on a PRAM (parallel random access machine) model. Our algorithm exhibits optimal speedup, in the sense that its processor-time product matches the worst-case time complexity of the fastest sequential algorithm.