Window subsequence problems for compressed texts

Authors:
Patrick Cégielski;Irène Guessarian;Yury Lifshits;Yuri Matiyasevich
Affiliations:
LACL, UMR-FRE 2673, Université Paris 12, Fontainebleau, France;LIAFA, UMR 7089 and Université Paris 6, Paris, France;Steklov Institute of Mathematics, St. Petersburg, Russia;Steklov Institute of Mathematics, St. Petersburg, Russia
Venue:
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Year:
2006

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Abstract

Given two strings (a text t of length n and a pattern p) and a natural number w, window subsequence problems consist in deciding whether p occurs as a subsequence of t and/or finding the number of size (at most) w windows of text t which contain pattern p as a subsequence, i.e. the letters of pattern p occur in the text window, in the same order as in p, but not necessarily consecutively (they may be interleaved with other letters). We are searching for subsequences in a text which is compressed using Lempel-Ziv-like compression algorithms, without decompressing the text, and we would like our algorithms to be almost optimal, in the sense that they run in time O(m) where m is the size of the compressed text. The pattern is uncompressed (because the compression algorithms are evolutive: various occurrences of a same pattern look different in the text).