Optimal parallel algorithms for forest and term matching

Forest matching is a fundamental step in solving various problems defined on terms such as term matching. We describe the first optimal speedup parallel algorithm for solving the forest matching problem. Our algorithm runs in time O(log n) using n log n processors on a CRCW PRAM, given a forest of n nodes as input. We use this algorithm to design the first optimal speedup parallel algorithm for solving the term matching problem. We also extend these algorithms to run on the weaker CREW PRAM with optimal speedup as well. This will involve a simple randomization scheme for simulating concurrent writes through a use of hashing.