Efficient computations of l1and l∞rearrangement distances

  • Authors:

  • Amihood Amir;Yonatan Aumann;Piotr Indyk;Avivit Levy;Ely Porat

  • Affiliations:

  • Department of Computer Science, Bar Ilan University, Ramat Gan, Israel and Department of Computer Science, Johns Hopkins University, Baltimore, MD;Department of Computer Science, Bar Ilan University, Ramat Gan, Israel;Department of Computter Science, MIT, Cambridge, Massachusetts;Department of Computer Science, Bar Ilan University, Ramat Gan, Israel;Department of Computer Science, Bar Ilan University, Ramat Gan, Israel

  • Venue:
  • SPIRE'07 Proceedings of the 14th international conference on String processing and information retrieval
  • Year:
  • 2007

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Abstract

Recently, a new pattern matching paradigm was proposed, pattern matching with address errors. In this paradigm approximate string matching problems are studied, where the content is unaltered and only the locations of the different entries may change. Specifically, a broad class of problems in this new paradigm was defined - the class of rearrangement errors. In this type of errors the pattern is transformed through a sequence of rearrangement operations, each with an associated cost. The natural l1 and l2 rearrangement systems were considered. A variant of the l1-rearrangement distance problem seems more difficult - where the pattern is a general string that may have repeating symbols. The best algorithm presented for the general case is O(nm). In this paper, we show that even for general strings the problem can be approximated in linear time! This paper also considers another natural rearrangement system - the l∞ rearrangement distance. For this new rearrangement system we provide efficient exact solutions for different variants of the problem, as well as a faster approximation.