Approximate Online Pattern Matching in Sublinear Time
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10404557" target="_blank" >RIV/00216208:11320/19:10404557 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4230/LIPIcs.FSTTCS.2019.10" target="_blank" >https://doi.org/10.4230/LIPIcs.FSTTCS.2019.10</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2019.10" target="_blank" >10.4230/LIPIcs.FSTTCS.2019.10</a>
Alternative languages
Result language
angličtina
Original language name
Approximate Online Pattern Matching in Sublinear Time
Original language description
We consider the approximate pattern matching problem under edit distance. In this problem we are given a pattern P of length m and a text T of length n over some alphabet Sigma, and a positive integer k. The goal is to find all the positions j in T such that there is a substring of T ending at j which has edit distance at most k from the pattern P. Recall, the edit distance between two strings is the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. For a position t in {1,...,n}, let k_t be the smallest edit distance between P and any substring of T ending at t. In this paper we give a constant factor approximation to the sequence k_1,k_2,...,k_n. We consider both offline and online settings. In the offline setting, where both P and T are available, we present an algorithm that for all t in {1,...,n}, computes the value of k_t approximately within a constant factor. The worst case running time of our algorithm is O~(n m^(3/4)). In the online setting, we are given P and then T arrives one symbol at a time. We design an algorithm that upon arrival of the t-th symbol of T computes k_t approximately within O(1)-multiplicative factor and m^(8/9)-additive error. Our algorithm takes O~(m^(1-(7/54))) amortized time per symbol arrival and takes O~(m^(1-(1/54))) additional space apart from storing the pattern P. Both of our algorithms are randomized and produce correct answer with high probability. To the best of our knowledge this is the first algorithm that takes worst-case sublinear (in the length of the pattern) time and sublinear extra space for the online approximate pattern matching problem. To get our result we build on the technique of Chakraborty, Das, Goldenberg, Koucký and Saks [FOCS'18] for computing a constant factor approximation of edit distance in sub-quadratic time.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GX19-27871X" target="_blank" >GX19-27871X: Efficient approximation algorithms and circuit complexity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
39th {IARCS} Annual Conference on Foundations of Software Technology and Theoretical Computer Science, {FSTTCS} 2019, December 11-13, 2019, Bombay, India
ISBN
978-3-95977-131-3
ISSN
1868-8969
e-ISSN
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Number of pages
15
Pages from-to
1-15
Publisher name
Schloss Dagstuhl - Leibniz-Zentrum fur Informatik
Place of publication
Dagstuhl, Germany
Event location
Bombay, India
Event date
Dec 11, 2019
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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