{"external_id":{"arxiv":["1704.02844"]},"date_published":"2017-01-01T00:00:00Z","abstract":[{"lang":"eng","text":"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).\r\n\r\nWe 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 ∊."}],"author":[{"last_name":"Bhattacharya","full_name":"Bhattacharya, Sayan","first_name":"Sayan"},{"first_name":"Monika H","full_name":"Henzinger, Monika H","last_name":"Henzinger","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530"},{"full_name":"Nanongkai, Danupon","first_name":"Danupon","last_name":"Nanongkai"}],"language":[{"iso":"eng"}],"_id":"11874","publication_status":"published","conference":{"end_date":"2017-01-19","name":"SODA: Symposium on Discrete Algorithms","location":"Barcelona, Spain","start_date":"2017-01-16"},"article_processing_charge":"No","main_file_link":[{"url":"https://arxiv.org/abs/1704.02844","open_access":"1"}],"date_created":"2022-08-16T12:28:27Z","extern":"1","date_updated":"2023-02-17T11:54:22Z","publication_identifier":{"eisbn":["978-161197478-2"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"470 - 489","volume":"0","oa":1,"month":"01","publication":"28th Annual ACM-SIAM Symposium on Discrete Algorithms","quality_controlled":"1","title":"Fully dynamic approximate maximum matching and minimum vertex cover in o(log3 n) worst case update time","oa_version":"Preprint","scopus_import":"1","status":"public","day":"01","citation":{"ista":"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.","ama":"Bhattacharya S, Henzinger MH, Nanongkai D. Fully dynamic approximate maximum matching and minimum vertex cover in o(log3 n) worst case update time. In: <i>28th Annual ACM-SIAM Symposium on Discrete Algorithms</i>. Vol 0. Society for Industrial and Applied Mathematics; 2017:470-489. doi:<a href=\"https://doi.org/10.1137/1.9781611974782.30\">10.1137/1.9781611974782.30</a>","mla":"Bhattacharya, Sayan, et al. “Fully Dynamic Approximate Maximum Matching and Minimum Vertex Cover in o(Log3 n) Worst Case Update Time.” <i>28th Annual ACM-SIAM Symposium on Discrete Algorithms</i>, vol. 0, Society for Industrial and Applied Mathematics, 2017, pp. 470–89, doi:<a href=\"https://doi.org/10.1137/1.9781611974782.30\">10.1137/1.9781611974782.30</a>.","short":"S. Bhattacharya, M.H. Henzinger, D. Nanongkai, in:, 28th Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2017, pp. 470–489.","apa":"Bhattacharya, S., Henzinger, M. H., &#38; Nanongkai, D. (2017). Fully dynamic approximate maximum matching and minimum vertex cover in o(log3 n) worst case update time. In <i>28th Annual ACM-SIAM Symposium on Discrete Algorithms</i> (Vol. 0, pp. 470–489). Barcelona, Spain: Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611974782.30\">https://doi.org/10.1137/1.9781611974782.30</a>","ieee":"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 <i>28th Annual ACM-SIAM Symposium on Discrete Algorithms</i>, Barcelona, Spain, 2017, vol. 0, pp. 470–489.","chicago":"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 <i>28th Annual ACM-SIAM Symposium on Discrete Algorithms</i>, 0:470–89. Society for Industrial and Applied Mathematics, 2017. <a href=\"https://doi.org/10.1137/1.9781611974782.30\">https://doi.org/10.1137/1.9781611974782.30</a>."},"year":"2017","type":"conference","publisher":"Society for Industrial and Applied Mathematics","doi":"10.1137/1.9781611974782.30"}