Distributed algorithms for tree pattern matching

Abstract

We present efficient distributed algorithms for the Tree Pattern Matching problem. To the best of our knowledge, these are the first distributed algorithms of this nature. Tree pattern matching is a fundamental operation in many programming task such as code optimization and automated theorem proving, and has a number of applications in distributed systems. We present both a top-down and bottom-up algorithm for linear tree pattern matching (where any variable occurs at most once in the pattern) for the case in which the subject tree is completely distributed as a node per processor. The pattern is assumed to reside within the local memory of each processor. Let the subject tree have n nodes and height h s , and the pattern m nodes and height h p . The top-down algorithm has bit complexity O(n log m h p ) and time complexity O(h s ), while the bottom-up algorithm has bit complexity O(n h p ) and time complexity O(h p ). However, the bottom-up algorithm requires preprocessing of the subject and pattern trees. An efficient extension of these distributed algorithms to the case of multiple patterns is also given.