Efficient computations of l1 and l∞ rearrangement distances

Authors:
Amihood Amir;Yonatan Aumann;Piotr Indyk;Avivit Levy;Ely Porat
Affiliations:
Department of Computer Science, Bar Ilan University, Ramat Gan 52900, Israel and Department of Computer Science, Johns Hopkins University, Baltimore, MD 21218, United States;Department of Computer Science, Bar Ilan University, Ramat Gan 52900, Israel;Department of Computer Science, MIT, Cambridge, MA 02139, United States;Department of Software Engineering, Shenkar College, 12 Anna Frank, Ramat-Gan, Israel and CRI, Haifa University, Mount Carmel, Haifa 31905, Israel;Department of Computer Science, Bar Ilan University, Ramat Gan 52900, Israel
Venue:
Theoretical Computer Science
Year:
2009

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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 was defined-the class of rearrangement errors. In this type of error the pattern is transformed through a sequence of rearrangement operations, each with an associated cost. The natural @?"1 and @?"2 rearrangement systems were considered. The best algorithm presented for general patterns, that may have repeating symbols, is O(nm). In this paper, we show that the problem can be approximated in linear time for general patterns! Another natural rearrangement system is considered in this paper-the @?"~ rearrangement distance. For this new rearrangement system efficient exact solutions for different variants of the problem are provided, as well as a faster approximation.