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Linear Time
Pattern Matching
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Optimal pattern matching in LZW compressed strings
Optimal pattern matching in LZW compressed strings,Pawel Gawrychowski
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Optimal pattern matching in LZW compressed strings
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Pawel Gawrychowski
We consider the following variant of the classical
pattern matching
problem: given an uncompressed pattern s[1..m] and a compressed representation of a string t[1..N], does s occur in t? When t is compressed using the LZW method, we are able to detect the occurrence in optimal linear time, thus answering a question of Amir, Benson, and Farach [2]. Previous results implied solutions with complexities O(n log m + m) [2], O(n + m1+ε) [14], or (randomized) O(n log N/n + m) [8], where n is the size of the compressed representation of t. Our algorithm is simple and fully deterministic.
Conference:
ACMSIAM Symposium on Discrete Algorithms  SODA
, pp. 362372, 2011
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