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Pattern matching in Lempel-Ziv compressed strings: fast, simple, and deterministic
[article]
<span title="2011-04-21">2011</span>
<i >
arXiv
</i>
<span class="release-stage" >pre-print</span>
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Countless variants of the Lempel-Ziv compression are widely used in many real-life applications. This paper is concerned with a natural modification of the classical pattern matching problem inspired by the popularity of such compression methods: given an uncompressed pattern s[1..m] and a Lempel-Ziv representation of a string t[1..N], does s occur in t? Farach and Thorup gave a randomized O(nlog^2(N/n)+m) time solution for this problem, where n is the size of the compressed representation of
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<a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1104.4203v1">arXiv:1104.4203v1</a>
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... We improve their result by developing a faster and fully deterministic O(nlog(N/n)+m) time algorithm with the same space complexity. Note that for highly compressible texts, log(N/n) might be of order n, so for such inputs the improvement is very significant. A (tiny) fragment of our method can be used to give an asymptotically optimal solution for the substring hashing problem considered by Farach and Muthukrishnan.
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