Efficient computations of ℓ1 and ℓ∞ rearrangement distances

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

doi:10.1007/978-3-540-75530-2_4

Efficient computations of ℓ₁ and ℓ_∞ rearrangement distances

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

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

13 Scopus citations

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.

Original language	English
Title of host publication	String Processing and Information Retrieval - 14th International Symposium, SPIRE 2007, Proceedings
Publisher	Springer Verlag
Pages	39-49
Number of pages	11
ISBN (Print)	9783540755296
DOIs	https://doi.org/10.1007/978-3-540-75530-2_4
State	Published - 2007
Event	14th International Symposium on String Processing and Information Retrieval, SPIRE 2007 - Santiago, Chile Duration: 29 Oct 2007 → 31 Oct 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4726 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	14th International Symposium on String Processing and Information Retrieval, SPIRE 2007
Country/Territory	Chile
City	Santiago
Period	29/10/07 → 31/10/07

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.

Funding

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.

Funders	Funder number
Iowa Science Foundation	35/05

Access to Document

10.1007/978-3-540-75530-2_4

Cite this

Amir, A., Aumann, Y., Indyk, P., Levy, A., & Porat, E. (2007). Efficient computations of ℓ₁ and ℓ_∞ rearrangement distances. In String Processing and Information Retrieval - 14th International Symposium, SPIRE 2007, Proceedings (pp. 39-49). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4726 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-75530-2_4

Amir, Amihood ; Aumann, Yonatan ; Indyk, Piotr et al. / Efficient computations of ℓ₁ and ℓ_∞ rearrangement distances. String Processing and Information Retrieval - 14th International Symposium, SPIRE 2007, Proceedings. Springer Verlag, 2007. pp. 39-49 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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.",

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Amir, A, Aumann, Y, Indyk, P, Levy, A & Porat, E 2007, Efficient computations of ℓ₁ and ℓ_∞ rearrangement distances. in String Processing and Information Retrieval - 14th International Symposium, SPIRE 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4726 LNCS, Springer Verlag, pp. 39-49, 14th International Symposium on String Processing and Information Retrieval, SPIRE 2007, Santiago, Chile, 29/10/07. https://doi.org/10.1007/978-3-540-75530-2_4

Efficient computations of ℓ₁ and ℓ_∞ rearrangement distances. / Amir, Amihood; Aumann, Yonatan; Indyk, Piotr et al.
String Processing and Information Retrieval - 14th International Symposium, SPIRE 2007, Proceedings. Springer Verlag, 2007. p. 39-49 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4726 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Amir A, Aumann Y, Indyk P, Levy A, Porat E. Efficient computations of ℓ₁ and ℓ_∞ rearrangement distances. In String Processing and Information Retrieval - 14th International Symposium, SPIRE 2007, Proceedings. Springer Verlag. 2007. p. 39-49. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-75530-2_4