We consider efficiency of NC-algorithms for pattern-searching in highly compressed one- and two-dimensional texts. “Highly compressed” means that the text can be exponentially large with respect to its compressed version, and “fast” means “in polylogarithmic time”. Given an uncompressed pattern P and a compressed version of a text T, the compressed matching problem is to test if P occurs in T. Two types of closely related compressed representations of 1-dimensional texts are considered: the Lempel-Ziv encodings (LZ, in short) and restricted LZ encodings (RLZ, in short). For highly compressed texts there is a small difference between them, in extreme situations both of them compress text exponentially, e.g. Fibonacci words of size N have compressed versions of size O(logN) for LZ and Restricted LZ encodings. Despite similarities we prove that LZ-compressed matching is P-complete while RLZ-compressed matching is rather trivially in NC. We show how to improve a naive straightforward NC algorithm and obtain almost optimal parallel RLZ-compressed matching applying tree-contraction techniques to directed acyclic graphs with polynomial tree-size. As a corollary we obtain an almost optimal parallel algorithm for LZW-compressed matching which is simpler than the (more general) algorithm in [11]. Highly compressed 2-dimensional texts are also considered.
CITATION STYLE
Gąsieniec, L., Gibbons, A., & Rytter, W. (1999). Efficiency of fast parallel pattern searching in highly compressed texts. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1672, pp. 48–58). Springer Verlag. https://doi.org/10.1007/3-540-48340-3_5
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