Shortest unique substring queries on run-length encoded strings

Takuya Mieno, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

We consider the problem of answering shortest unique substring (SUS) queries on run-length encoded strings. For a string S, a unique substring u = S[i..j] is said to be a shortest unique substring (SUS) of S containing an interval [s, t] (i ≤ s ≤ t ≤ j) if for any i0 ≤ s ≤t ≤j0 with j - i > j0 - i0, S[i0..j0] occurs at least twice in S. Given a run-length encoding of size m of a string of length N, we show that we can construct a data structure of size O(m + πs(N,m)) in O(mlogm + πc(N,m)) time such that queries can be answered in O(πq(N,m) + k) time, where k is the size of the output (the number of SUSs), and πs(N,m), πc(N,m), πq(N,m) are, respectively, the size, construction time, and query time for a predecessor/successor query data structure of m elements for the universe of [1,N]. Using the data structure by Beam and Fich (JCSS 2002), this results in a data structure of O(m) space that is constructed in O(mlogm) time, and answers queries in O( √ log m/log logm + k) time.

Original languageEnglish
Title of host publication41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016
EditorsAnca Muscholl, Piotr Faliszewski, Rolf Niedermeier
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770163
DOIs
Publication statusPublished - Aug 1 2016
Event41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 - Krakow, Poland
Duration: Aug 22 2016Aug 26 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume58
ISSN (Print)1868-8969

Other

Other41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016
CountryPoland
CityKrakow
Period8/22/168/26/16

All Science Journal Classification (ASJC) codes

  • Software

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  • Cite this

    Mieno, T., Inenaga, S., Bannai, H., & Takeda, M. (2016). Shortest unique substring queries on run-length encoded strings. In A. Muscholl, P. Faliszewski, & R. Niedermeier (Eds.), 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 [69] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 58). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.MFCS.2016.69