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Deterministic fully dynamic data structures for vertex cover and matching

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Bhattacharya, Sayan, Henzinger, Monika and Italiano, Giuseppe F. (2018) Deterministic fully dynamic data structures for vertex cover and matching. SIAM Journal on Computing, 47 (3). pp. 859-887. doi:10.1137/140998925 ISSN 0097-5397.

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Official URL: http://dx.doi.org/10.1137/140998925

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Abstract

We present the first deterministic data structures for maintaining approximate minimum vertex cover and maximum matching in a fully dynamic graph in time per update. In particular, for minimum vertex cover we provide deterministic data structures for maintaining a (2 + ε) approximation in O(log n/ε2) amortized time per update. For maximum matching, we show how to maintain a (3 + e) approximation in O(m1/3/ε2) amortized time per update, and a (4 + ε) approximation in O(m1/3/ε2) worst-case time per update. Our data structure for fully dynamic minimum vertex cover is essentially near-optimal and settles an open problem by Onak and Rubinfeld [13].

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH): Vertex operator algebras, Algorithms, Data structures (Computer science) -- Mathematical models
Journal or Publication Title: SIAM Journal on Computing
Publisher: Society for Industrial and Applied Mathematics
ISSN: 0097-5397
Official Date: 2018
Dates:
DateEvent
2018Published
28 March 2018Accepted
Volume: 47
Number: 3
Page Range: pp. 859-887
DOI: 10.1137/140998925
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): “First Published in SIAM Journal on Computing in 47(3) 2018 published by the Society for Industrial and Applied Mathematics (SIAM)” “Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.”)
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 19 November 2019
Date of first compliant Open Access: 19 November 2019
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
340506Seventh Framework Programmehttp://dx.doi.org/10.13039/100011102
317532Seventh Framework Programmehttp://dx.doi.org/10.13039/100011102
AMANDA Ministero dell’Istruzione, dell’Università e della Ricercahttp://dx.doi.org/10.13039/501100003407
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