Efficient computations of ℓ[subscript 1] and ℓ[subscript ∞] rearrangement distances
Author(s)Amir, Amihood; Aumann, Yonatan; Indyk, Piotr; Levy, Avivit; Porat, Ely
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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 ℓ[subscript 1] and ℓ[subscript 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 ℓ[subscript ∞] rearrangement distance. For this new rearrangement system efficient exact solutions for different variants of the problem are provided, as well as a faster approximation.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Theoretical Computer Science
Amir, Amihood, Yonatan Aumann, Piotr Indyk, Avivit Levy, and Ely Porat. “Efficient computations of ℓ[subscript 1] and ℓ[subscript ∞] rearrangement distances.” Theoretical Computer Science 410, no. 43 (October 2009): 4382–4390. © 2009 Elsevier B.V.
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