Fully dynamic approximate maximum matching and minimum vertex cover in o(log3 n) worst case update time

Bhattacharya S, Henzinger MH, Nanongkai D. 2017. Fully dynamic approximate maximum matching and minimum vertex cover in o(log3 n) worst case update time. 28th Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms vol. 0, 470–489.

Download (ext.)

Conference Paper | Published | English

Scopus indexed
Author
Bhattacharya, Sayan; Henzinger, MonikaISTA ; Nanongkai, Danupon
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 ∊.
Publishing Year
Date Published
2017-01-01
Proceedings Title
28th Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher
Society for Industrial and Applied Mathematics
Page
470 - 489
Conference
SODA: Symposium on Discrete Algorithms
Conference Location
Barcelona, Spain
Conference Date
2017-01-16 – 2017-01-19
IST-REx-ID

Cite this

Bhattacharya S, Henzinger MH, Nanongkai D. Fully dynamic approximate maximum matching and minimum vertex cover in o(log3 n) worst case update time. In: 28th Annual ACM-SIAM Symposium on Discrete Algorithms. Vol 0. Society for Industrial and Applied Mathematics; 2017:470-489. doi:10.1137/1.9781611974782.30
Bhattacharya, S., Henzinger, M. H., & Nanongkai, D. (2017). Fully dynamic approximate maximum matching and minimum vertex cover in o(log3 n) worst case update time. In 28th Annual ACM-SIAM Symposium on Discrete Algorithms (Vol. 0, pp. 470–489). Barcelona, Spain: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611974782.30
Bhattacharya, Sayan, Monika H Henzinger, and Danupon Nanongkai. “Fully Dynamic Approximate Maximum Matching and Minimum Vertex Cover in o(Log3 n) Worst Case Update Time.” In 28th Annual ACM-SIAM Symposium on Discrete Algorithms, 0:470–89. Society for Industrial and Applied Mathematics, 2017. https://doi.org/10.1137/1.9781611974782.30.
S. Bhattacharya, M. H. Henzinger, and D. Nanongkai, “Fully dynamic approximate maximum matching and minimum vertex cover in o(log3 n) worst case update time,” in 28th Annual ACM-SIAM Symposium on Discrete Algorithms, Barcelona, Spain, 2017, vol. 0, pp. 470–489.
Bhattacharya S, Henzinger MH, Nanongkai D. 2017. Fully dynamic approximate maximum matching and minimum vertex cover in o(log3 n) worst case update time. 28th Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms vol. 0, 470–489.
Bhattacharya, Sayan, et al. “Fully Dynamic Approximate Maximum Matching and Minimum Vertex Cover in o(Log3 n) Worst Case Update Time.” 28th Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 0, Society for Industrial and Applied Mathematics, 2017, pp. 470–89, doi:10.1137/1.9781611974782.30.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data ISTA Research Explorer

Sources

arXiv 1704.02844

Search this title in

Google Scholar