Juha Kärkkäinen, Dominik Kempa and Simon J. Puglisi

**Crochemore's String Matching Algorithm: Simplification, Extensions, Applications**

Abstract: |

We address the problem of string matching in the special case where the pattern is very long. First, constant extra space algorithms are desirable with long patterns, and we describe a simplified version of Crochemore's algorithm retaining its linear time complexity and constant extra space usage. Second, long patterns are unlikely to occur in the text at all. Thus we define a generalization of string matching called Longest Prefix Matching that asks for the occurrences of the longest prefix of the pattern occurring in the text at least once, and modify the simplified Crochemore's algorithm to solve this problem. Finally, we define and solve the problem of Sparse Longest Prefix Matching that is useful when the pattern has to be split into multiple pieces because it is too long to be processed in one piece. These problems are motivated by and have application in Lempel-Ziv (LZ77) factorization. |

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