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Deterministic rounding of dynamic fractional matchings
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Bhattacharya, Sayan and Kiss, Peter (2021) Deterministic rounding of dynamic fractional matchings. In: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021), Virtual, 12-16 Jul 2021. Published in: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021), 198 27:1-27:14. ISBN 9783959771955. doi:10.4230/LIPIcs.ICALP.2021.27 ISSN 1868-8969.
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Official URL: https://doi.org/10.4230/LIPIcs.ICALP.2021.27
Abstract
We present a framework for deterministically rounding a dynamic fractional matching. Applying our framework in a black-box manner on top of existing fractional matching algorithms, we derive the following new results: (1) The first deterministic algorithm for maintaining a (2-δ)-approximate maximum matching in a fully dynamic bipartite graph, in arbitrarily small polynomial update time. (2) The first deterministic algorithm for maintaining a (1+δ)-approximate maximum matching in a decremental bipartite graph, in polylogarithmic update time. (3) The first deterministic algorithm for maintaining a (2+δ)-approximate maximum matching in a fully dynamic general graph, in small polylogarithmic (specifically, O(log⁴ n)) update time. These results are respectively obtained by applying our framework on top of the fractional matching algorithms of Bhattacharya et al. [STOC'16], Bernstein et al. [FOCS'20], and Bhattacharya and Kulkarni [SODA'19].
Previously, there were two known general-purpose rounding schemes for dynamic fractional matchings. Both these schemes, by Arar et al. [ICALP'18] and Wajc [STOC'20], were randomized.
Our rounding scheme works by maintaining a good matching-sparsifier with bounded arboricity, and then applying the algorithm of Peleg and Solomon [SODA'16] to maintain a near-optimal matching in this low arboricity graph. To the best of our knowledge, this is the first dynamic matching algorithm that works on general graphs by using an algorithm for low-arboricity graphs as a black-box subroutine. This feature of our rounding scheme might be of independent interest.
Item Type: | Conference Item (Paper) | ||||||
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Subjects: | Q Science > QA Mathematics T Technology > T Technology (General) |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||
Library of Congress Subject Headings (LCSH): | Dynamic programming, Computer algorithms, Approximation theory | ||||||
Series Name: | Leibniz International Proceedings in Informatics (LIPIcs) | ||||||
Journal or Publication Title: | 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021) | ||||||
Publisher: | Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik | ||||||
ISBN: | 9783959771955 | ||||||
ISSN: | 1868-8969 | ||||||
Official Date: | 2 July 2021 | ||||||
Dates: |
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Volume: | 198 | ||||||
Page Range: | 27:1-27:14 | ||||||
DOI: | 10.4230/LIPIcs.ICALP.2021.27 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 12 May 2020 | ||||||
Date of first compliant Open Access: | 14 May 2020 | ||||||
RIOXX Funder/Project Grant: |
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Conference Paper Type: | Paper | ||||||
Title of Event: | 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021) | ||||||
Type of Event: | Conference | ||||||
Location of Event: | Virtual | ||||||
Date(s) of Event: | 12-16 Jul 2021 | ||||||
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Open Access Version: |
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