Generalized Substring Compression

  • Authors:

  • Orgad Keller;Tsvi Kopelowitz;Shir Landau;Moshe Lewenstein

  • Affiliations:

  • Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel 52900;Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel 52900;Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel 52900;Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel 52900

  • Venue:
  • CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
  • Year:
  • 2009

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Abstract

In substring compression one is given a text to preprocess so that, upon request, a compressed substring is returned. Generalized substring compression is the same with the following twist. The queries contain an additional context substring (or a collection of context substrings) and the answers are the substring in compressed format, where the context substring is used to make the compression more efficient. We focus our attention on generalized substring compression and present the first non-trivial correct algorithm for this problem. In our algorithm we inherently propose a method for finding the bounded longest common prefix of substrings, which may be of independent interest. In addition, we propose an efficient algorithm for substring compression which makes use of range searching for minimum queries. We present several tradeoffs for both problems. For compressing the substring S [i . . j ] (possibly with the substring S [*** . . β ] as a context), best query times we achieve are O (C ) and $O\big(C\log\big(\frac{j-i}{C}\big)\big)$ for substring compression query and generalized substring compression query, respectively, where C is the number of phrases encoded.