Fast entropy-bounded string dictionary look-up with mismatches

Paweł Gawrychowski; Gad M. Landau; Tatiana Starikovskaya

doi:10.4230/LIPIcs.MFCS.2018.66

Fast entropy-bounded string dictionary look-up with mismatches

Paweł Gawrychowski, Gad M. Landau, Tatiana Starikovskaya

Department of Computer Science

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

Abstract

We revisit the fundamental problem of dictionary look-up with mismatches. Given a set (dictionary) of d strings of length m and an integer k, we must preprocess it into a data structure to answer the following queries: Given a query string Q of length m, find all strings in the dictionary that are at Hamming distance at most k from Q. Chan and Lewenstein (CPM 2015) showed a data structure for k = 1 with optimal query time O(m/w + occ), where w is the size of a machine word and occ is the size of the output. The data structure occupies O(wd log^1+ε d) extra bits of space (beyond the entropy-bounded space required to store the dictionary strings). In this work we give a solution with similar bounds for a much wider range of values k. Namely, we give a data structure that has O(m/w + log^k d + occ) query time and uses O(wd log^k d) extra bits of space.

Original language	English
Title of host publication	43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018
Editors	Igor Potapov, James Worrell, Paul Spirakis
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Print)	9783959770866
DOIs	https://doi.org/10.4230/LIPIcs.MFCS.2018.66
State	Published - 1 Aug 2018
Event	43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018 - Liverpool, United Kingdom Duration: 27 Aug 2018 → 31 Aug 2018

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	117
ISSN (Print)	1868-8969

Conference

Conference	43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018
Country/Territory	United Kingdom
City	Liverpool
Period	27/08/18 → 31/08/18

Bibliographical note

Publisher Copyright:
© Paweł Gawrychowski, Gad M. Landau, and Tatiana Starikovskaya.

Keywords

Compact data structures
Dictionary look-up
Hamming distance

ASJC Scopus subject areas

Software

Access to Document

10.4230/LIPIcs.MFCS.2018.66

Cite this

Gawrychowski, P., Landau, G. M., & Starikovskaya, T. (2018). Fast entropy-bounded string dictionary look-up with mismatches. In I. Potapov, J. Worrell, & P. Spirakis (Eds.), 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018 Article 66 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 117). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.MFCS.2018.66

Gawrychowski, Paweł ; Landau, Gad M. ; Starikovskaya, Tatiana. / Fast entropy-bounded string dictionary look-up with mismatches. 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018. editor / Igor Potapov ; James Worrell ; Paul Spirakis. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. (Leibniz International Proceedings in Informatics, LIPIcs).

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title = "Fast entropy-bounded string dictionary look-up with mismatches",

abstract = "We revisit the fundamental problem of dictionary look-up with mismatches. Given a set (dictionary) of d strings of length m and an integer k, we must preprocess it into a data structure to answer the following queries: Given a query string Q of length m, find all strings in the dictionary that are at Hamming distance at most k from Q. Chan and Lewenstein (CPM 2015) showed a data structure for k = 1 with optimal query time O(m/w + occ), where w is the size of a machine word and occ is the size of the output. The data structure occupies O(wd log1+ε d) extra bits of space (beyond the entropy-bounded space required to store the dictionary strings). In this work we give a solution with similar bounds for a much wider range of values k. Namely, we give a data structure that has O(m/w + logk d + occ) query time and uses O(wd logk d) extra bits of space.",

keywords = "Compact data structures, Dictionary look-up, Hamming distance",

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note = "Publisher Copyright: {\textcopyright} Pawe{\l} Gawrychowski, Gad M. Landau, and Tatiana Starikovskaya.; 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018 ; Conference date: 27-08-2018 Through 31-08-2018",

year = "2018",

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doi = "10.4230/LIPIcs.MFCS.2018.66",

language = "English",

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Gawrychowski, P, Landau, GM & Starikovskaya, T 2018, Fast entropy-bounded string dictionary look-up with mismatches. in I Potapov, J Worrell & P Spirakis (eds), 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018., 66, Leibniz International Proceedings in Informatics, LIPIcs, vol. 117, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018, Liverpool, United Kingdom, 27/08/18. https://doi.org/10.4230/LIPIcs.MFCS.2018.66

Fast entropy-bounded string dictionary look-up with mismatches. / Gawrychowski, Paweł; Landau, Gad M.; Starikovskaya, Tatiana.
43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018. ed. / Igor Potapov; James Worrell; Paul Spirakis. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. 66 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 117).

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

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N2 - We revisit the fundamental problem of dictionary look-up with mismatches. Given a set (dictionary) of d strings of length m and an integer k, we must preprocess it into a data structure to answer the following queries: Given a query string Q of length m, find all strings in the dictionary that are at Hamming distance at most k from Q. Chan and Lewenstein (CPM 2015) showed a data structure for k = 1 with optimal query time O(m/w + occ), where w is the size of a machine word and occ is the size of the output. The data structure occupies O(wd log1+ε d) extra bits of space (beyond the entropy-bounded space required to store the dictionary strings). In this work we give a solution with similar bounds for a much wider range of values k. Namely, we give a data structure that has O(m/w + logk d + occ) query time and uses O(wd logk d) extra bits of space.

AB - We revisit the fundamental problem of dictionary look-up with mismatches. Given a set (dictionary) of d strings of length m and an integer k, we must preprocess it into a data structure to answer the following queries: Given a query string Q of length m, find all strings in the dictionary that are at Hamming distance at most k from Q. Chan and Lewenstein (CPM 2015) showed a data structure for k = 1 with optimal query time O(m/w + occ), where w is the size of a machine word and occ is the size of the output. The data structure occupies O(wd log1+ε d) extra bits of space (beyond the entropy-bounded space required to store the dictionary strings). In this work we give a solution with similar bounds for a much wider range of values k. Namely, we give a data structure that has O(m/w + logk d + occ) query time and uses O(wd logk d) extra bits of space.

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ER -

Gawrychowski P, Landau GM, Starikovskaya T. Fast entropy-bounded string dictionary look-up with mismatches. In Potapov I, Worrell J, Spirakis P, editors, 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2018. 66. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.MFCS.2018.66

Fast entropy-bounded string dictionary look-up with mismatches

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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