Efficient algorithms to compute compressed longest common substrings and compressed palindromes

Authors:
Wataru Matsubara;Shunsuke Inenaga;Akira Ishino;Ayumi Shinohara;Tomoyuki Nakamura;Kazuo Hashimoto
Affiliations:
Graduate School of Information Sciences, Tohoku University, Japan;Graduate School of Information Science and Electrical Engineering, Kyushu University, Japan;Graduate School of Information Sciences, Tohoku University, Japan;Graduate School of Information Sciences, Tohoku University, Japan;Graduate School of Information Sciences, Tohoku University, Japan;Graduate School of Information Sciences, Tohoku University, Japan
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

This paper studies two problems on compressed strings described interms of straight line programs (SLPs). One is tocompute the length of the longest common substring of two givenSLP-compressed strings, and the other is to compute all palindromesof a given SLP-compressed string. In order to solve these problemsefficiently (in polynomial time w.r.t. the compressed size)decompression is never feasible, since the decompressed size can beexponentially large. We develop combinatorial algorithms that solvethese problems in O(n4logn) timewith O(n3) space, and inO(n4) time withO(n2) space, respectively, where nis the size of the input SLP-compressed strings.