Efficient computations of ℓ1 and ℓ rearrangement distances

Amihood Amir, Yonatan Aumann, Piotr Indyk, Avivit Levy, Ely Porat

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 ℓ1 and ℓ2 rearrangement systems were considered. The best algorithm presented for general patterns, that may have repeating symbols, is O (n m). 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 ℓ rearrangement distance. For this new rearrangement system efficient exact solutions for different variants of the problem are provided, as well as a faster approximation.

Original languageEnglish
Pages (from-to)4382-4390
Number of pages9
JournalTheoretical Computer Science
Issue number43
StatePublished - 6 Oct 2009

Bibliographical note

Funding Information:
The authors wish to thank the anonymous referees who carefully read the original manuscript and provided comments that were invaluable to the flow and understandability of the paper. First author was partly supported by ISF grant 35/05.


  • Approximate string matching
  • Pattern matching
  • Rearrangement distances


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