Abstract
We show an efficient pattern-matching algorithm for strings that are succinctly described in terms of straight-line programs, in which the constants are symbols and the only operation is the concatenation. In this paper, both text T and pattern P are given by straight-line programs T and P. The length of the text T (pattern P, resp.) may grow exponentially with respect to its description size âTâ=n (âpâ=m, resp.). We show a new combinatorial property concerning with the periodic occurrences of a pattern in a text. Based on this property, we develop an O(n 2 m 2) time algorithm using O(nm) space, which outputs a compact representation of all occurrences of P in T. This is superior to the algorithm proposed by Karpinski et al. [11], which runs in O((n+m) 4 log (n+m)) time using O((n+m)3) space, and finds only one occurrence. Moreover, our algorithm is much simpler than theirs.
This research was supported in part by Grant-in-Aid for Scientific Research (A) from the Ministry of Education, Science, Sports and Culture, Japan, No. 07558051.
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Miyazaki, M., Shinohara, A., Takeda, M. (1997). An improved pattern matching algorithm for strings in terms of straight-line programs. In: Apostolico, A., Hein, J. (eds) Combinatorial Pattern Matching. CPM 1997. Lecture Notes in Computer Science, vol 1264. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63220-4_45
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DOI: https://doi.org/10.1007/3-540-63220-4_45
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