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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2017.26
URN: urn:nbn:de:0030-drops-73189
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7318/
Amir, Amihood ;
Levy, Avivit ;
Lubin, Ronit ;
Porat, Ely
Approximate Cover of Strings
Abstract
Regularities in strings arise in various areas of science, including coding and automata theory, formal language theory, combinatorics, molecular biology and many others. A common notion to describe regularity in a string T is a cover, which is a string C for which every letter of T lies within some occurrence of C. The alignment of the cover repetitions in the given text is called a tiling. In many applications finding exact repetitions is not sufficient, due to the presence of errors. In this paper, we use a new approach for handling errors in coverable phenomena and define the approximate cover problem (ACP), in which we are given a text that is a sequence of some cover repetitions with possible mismatch errors, and we seek a string that covers the text with the minimum number of errors. We first show that the ACP is NP-hard, by studying the cover-size relaxation of the ACP, in which the requested size of the approximate cover is also given with the input string. We show this relaxation is already NP-hard. We also study another two relaxations of the ACP, which we call the partial-tiling relaxation of the ACP and the full-tiling relaxation of the ACP, in which a tiling of the requested cover is also given with the input string. A given full tiling retains all the occurrences of the cover before the errors, while in a partial tiling there can be additional occurrences of the cover that are not marked by the tiling. We show that the partial-tiling relaxation has a polynomial time complexity and give experimental evidence that the full-tiling also has polynomial time complexity. The study of these relaxations, besides shedding another light on the complexity of the ACP, also involves a deep understanding of the properties of covers, yielding some key lemmas and observations that may be helpful for a future study of regularities in the presence of errors.
BibTeX - Entry
@InProceedings{amir_et_al:LIPIcs:2017:7318,
author = {Amihood Amir and Avivit Levy and Ronit Lubin and Ely Porat},
title = {{Approximate Cover of Strings}},
booktitle = {28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
pages = {26:1--26:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-039-2},
ISSN = {1868-8969},
year = {2017},
volume = {78},
editor = {Juha K{\"a}rkk{\"a}inen and Jakub Radoszewski and Wojciech Rytter},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7318},
URN = {urn:nbn:de:0030-drops-73189},
doi = {10.4230/LIPIcs.CPM.2017.26},
annote = {Keywords: periodicity, quasi-periodicity, cover, approximate cover}
}
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Keywords: |
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periodicity, quasi-periodicity, cover, approximate cover |
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Collection: |
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28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017) |
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Issue Date: |
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2017 |
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Date of publication: |
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30.06.2017 |
