A Distributed Context-Free Language Constrained Shortest Path Algorithm

Abstract

Formal language constrained shortest path problems are concerned with finding shortest paths in labeled graphs. These labeled paths have the constraint that the concatenation of labels along a path constitute a valid string in some formal language Lambda over alphabet Sigma. These problems are well studied where the formal language is regular or context-free, and have been used in a variety of applications ranging from databases, to transportation planning, to programming languages. Barrett, Jacob, and Marathe's best algorithm for the context-free language constrained path problem runs in O(|V|3|N||P|) time, where N is the set of non-terminals for the input grammar and P is the set of productions (expressed in Chomsky Normal Form). We present a work and time efficient distributed version of this algorithm that may be distributed on up to O(|V||N|) nodes.