Improving time and space complexity for compressed pattern matching

Authors:
Shirou Maruyama;Hiromitsu Miyagawa;Hiroshi Sakamoto
Affiliations:
Graduate School of Computer Science and Systems Engineering;Graduate School of Computer Science and Systems Engineering;Faculty of Computer Science and Systems Engineering, Kyushu Institute of Technology, Iizuka, Japan
Venue:
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Year:
2006

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Abstract

The compressed pattern matching problem is to find all occurrences of a given pattern in a compressed text. In this paper an efficient grammar-based compression algorithm is presented for the compressed pattern matching. The algorithm achieves the worst-case approximation ratio O(g*logg*logn) for the optimum grammar size g* with an input text of length n. This upper bound improves the complexity of the compressed pattern matching problem to $O(g_*\log g_*\log m + \frac{n}{m} + m^2 + r)$ time and O(g*logg*logm + m2) space for any pattern shorter than m and the number r of pattern occurrences.