Efficient algorithms to compute compressed longest common substrings and compressed palindromes

Wataru Matsubara, Shunsuke Inenaga, Akira Ishino, Ayumi Shinohara, Tomoyuki Nakamura, Kazuo Hashimoto

Research output: Contribution to journalArticlepeer-review

58 Citations (Scopus)


This paper studies two problems on compressed strings described in terms of straight line programs (SLPs). One is to compute the length of the longest common substring of two given SLP-compressed strings, and the other is to compute all palindromes of a given SLP-compressed string. In order to solve these problems efficiently (in polynomial time w.r.t. the compressed size) decompression is never feasible, since the decompressed size can be exponentially large. We develop combinatorial algorithms that solve these problems in O (n4 log n) time with O (n3) space, and in O (n4) time with O (n2) space, respectively, where n is the size of the input SLP-compressed strings.

Original languageEnglish
Pages (from-to)900-913
Number of pages14
JournalTheoretical Computer Science
Issue number8-10
Publication statusPublished - 2009 Mar 1


  • Longest common substring
  • Palindromes
  • Straight line program
  • String processing algorithms
  • Text compression


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