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Fully dynamic approximate maximum matching and minimum vertex cover in O(log3 n) worst case update time
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Bhattacharya, Sayan, Henzinger, Monika and Nanongkai, Danupon (2017) Fully dynamic approximate maximum matching and minimum vertex cover in O(log3 n) worst case update time. In: Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, Barcelona, Spain, 16-19 Jan 2017. Published in: Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms pp. 470-489. ISBN 9781611974782. doi:10.1137/1.9781611974782.30
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Official URL: http://dx.doi.org/10.1137/1.9781611974782.30
Abstract
We consider the problem of maintaining an approximately maximum (fractional) matching and an approximately minimum vertex cover in a dynamic graph. Starting with the seminal paper by Onak and Rubinfeld [STOC 2010], this problem has received significant attention in recent years. There remains, however, a polynomial gap between the best known worst case update time and the best known amortised update time for this problem, even after allowing for randomisation. Specifically, Bernstein and Stein [ICALP 2015, SODA 2016] have the best known worst case update time. They present a deterministic data structure with approximation ratio (3/2 + ∊) and worst case update time O(m1/4/ ∊2), where m is the number of edges in the graph. In recent past, Gupta and Peng [FOCS 2013] gave a deterministic data structure with approximation ratio (1+ ∊) and worst case update time No known randomised data structure beats the worst case update times of these two results. In contrast, the paper by Onak and Rubinfeld [STOC 2010] gave a randomised data structure with approximation ratio O(1) and amortised update time O(log2 n), where n is the number of nodes in the graph. This was later improved by Baswana, Gupta and Sen [FOCS 2011] and Solomon [FOCS 2016], leading to a randomised date structure with approximation ratio 2 and amortised update time O(1).
We bridge the polynomial gap between the worst case and amortised update times for this problem, without using any randomisation. We present a deterministic data structure with approximation ratio (2 + ∊) and worst case update time O(log3 n), for all sufficiently small constants ∊.
| Item Type: | Conference Item (Paper) | |||||||||
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| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | |||||||||
| Divisions: | Faculty of Science > Computer Science | |||||||||
| Library of Congress Subject Headings (LCSH): | Graph algorithms, Graph theory | |||||||||
| Journal or Publication Title: | Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms | |||||||||
| Publisher: | SIAM | |||||||||
| ISBN: | 9781611974782 | |||||||||
| Book Title: | Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms | |||||||||
| Official Date: | 2017 | |||||||||
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| Page Range: | pp. 470-489 | |||||||||
| DOI: | 10.1137/1.9781611974782.30 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access | |||||||||
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| Conference Paper Type: | Paper | |||||||||
| Title of Event: | Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms | |||||||||
| Type of Event: | Conference | |||||||||
| Location of Event: | Barcelona, Spain | |||||||||
| Date(s) of Event: | 16-19 Jan 2017 |
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