Abstract
Our main result in this paper is a parallel algorithm for suffix--prefix- (s--p-) matching that has optimal speedup on a concurrent-read/concurrent-write parallel random-access machine (CRCW PRAM). Given a string of length $m$, the algorithm runs in time $O(\log m)$ using $m/ \log m$ processors. This algorithm is important because we utilize s--p matching as a fundamental building block to solve several pattern- and string-matching problems, such as the following: {1. string matching; 2. multitext/multipattern string matching; 3. multidimensional pattern matching; 4. pattern-occurrence detection; 5. on-line string matching.} In particular, our techniques and algorithms are the first to preserve optimal speedup in the context of pattern matching in higher dimensions and are the only known ones to do so for dimensions $d > 2$.
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