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Fully Dynamic Approximate Maximum Matching and Minimum Vertex Cover in O(log(3) n) Worst Case Update TimePrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2017 (English)In: PROCEEDINGS OF THE TWENTY-EIGHTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, ASSOC COMPUTING MACHINERY , 2017, p. 470-489Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

ASSOC COMPUTING MACHINERY , 2017. p. 470-489
##### National Category

Electrical Engineering, Electronic Engineering, Information Engineering
##### Identifiers

URN: urn:nbn:se:kth:diva-228294ISI: 000426965800030Scopus ID: 2-s2.0-85016184685OAI: oai:DiVA.org:kth-228294DiVA, id: diva2:1208974
##### Conference

28th Annual ACM-SIAM Symposium on Discrete Algoritms, Barcelona, SPAIN JAN 16-19, 2017
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt451",{id:"formSmash:j_idt451",widgetVar:"widget_formSmash_j_idt451",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt457",{id:"formSmash:j_idt457",widgetVar:"widget_formSmash_j_idt457",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt463",{id:"formSmash:j_idt463",widgetVar:"widget_formSmash_j_idt463",multiple:true});
##### Note

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 + epsilon) and worst case update time O(m(1/4)/epsilon(2)) where m is the number of edges in the graph. In recent past, Gupta and Peng [FOGS 2013] gave a deterministic data structure with approximation ratio (1 + epsilon) and worst case update time O(root mT/epsilon(2)). 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(log(2) n), where n is the number of nodes in the graph. This was later improved by Baswana, Gupta and Sen [FOGS 2011] and Solomon [FOGS 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 + epsilon) and worst case update time O(log(3) n), for all sufficiently small constants epsilon.

QC 20180521

Available from: 2018-05-21 Created: 2018-05-21 Last updated: 2018-05-21Bibliographically approved
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