{"main_file_link":[{"url":"https://doi.org/10.1007/s00453-019-00630-4","open_access":"1"}],"title":"Deterministic dynamic matching in O(1) update time","scopus_import":"1","quality_controlled":"1","issue":"4","oa_version":"Published Version","intvolume":"        82","language":[{"iso":"eng"}],"year":"2020","publisher":"Springer Nature","article_type":"original","day":"01","date_published":"2020-04-01T00:00:00Z","keyword":["Dynamic algorithms","Data structures","Graph algorithms","Matching","Vertex cover"],"author":[{"last_name":"Bhattacharya","first_name":"Sayan","full_name":"Bhattacharya, Sayan"},{"last_name":"Chakrabarty","first_name":"Deeparnab","full_name":"Chakrabarty, Deeparnab"},{"last_name":"Henzinger","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530"}],"doi":"10.1007/s00453-019-00630-4","_id":"11675","publication":"Algorithmica","publication_status":"published","abstract":[{"text":"We consider the problems of maintaining an approximate maximum matching and an approximate minimum vertex cover in a dynamic graph undergoing a sequence of edge insertions/deletions. Starting with the seminal work of Onak and Rubinfeld (in: Proceedings of the ACM symposium on theory of computing (STOC), 2010), this problem has received significant attention in recent years. Very recently, extending the framework of Baswana et al. (in: Proceedings of the IEEE symposium on foundations of computer science (FOCS), 2011) , Solomon (in: Proceedings of the IEEE symposium on foundations of computer science (FOCS), 2016) gave a randomized dynamic algorithm for this problem that has an approximation ratio of 2 and an amortized update time of O(1) with high probability. This algorithm requires the assumption of an oblivious adversary, meaning that the future sequence of edge insertions/deletions in the graph cannot depend in any way on the algorithm’s past output. A natural way to remove the assumption on oblivious adversary is to give a deterministic dynamic algorithm for the same problem in O(1) update time. In this paper, we resolve this question. We present a new deterministic fully dynamic algorithm that maintains a O(1)-approximate minimum vertex cover and maximum fractional matching, with an amortized update time of O(1). Previously, the best deterministic algorithm for this problem was due to Bhattacharya et al. (in: Proceedings of the ACM-SIAM symposium on discrete algorithms (SODA), 2015); it had an approximation ratio of (2+ε) and an amortized update time of O(logn/ε2). Our result can be generalized to give a fully dynamic O(f3)-approximate algorithm with O(f2) amortized update time for the hypergraph vertex cover and fractional hypergraph matching problem, where every hyperedge has at most f vertices.","lang":"eng"}],"volume":82,"date_updated":"2022-09-12T08:55:46Z","type":"journal_article","extern":"1","publication_identifier":{"issn":["0178-4617"],"eissn":["1432-0541"]},"page":"1057-1080","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"article_processing_charge":"No","citation":{"ieee":"S. Bhattacharya, D. Chakrabarty, and M. H. Henzinger, “Deterministic dynamic matching in O(1) update time,” <i>Algorithmica</i>, vol. 82, no. 4. Springer Nature, pp. 1057–1080, 2020.","mla":"Bhattacharya, Sayan, et al. “Deterministic Dynamic Matching in O(1) Update Time.” <i>Algorithmica</i>, vol. 82, no. 4, Springer Nature, 2020, pp. 1057–80, doi:<a href=\"https://doi.org/10.1007/s00453-019-00630-4\">10.1007/s00453-019-00630-4</a>.","ama":"Bhattacharya S, Chakrabarty D, Henzinger MH. Deterministic dynamic matching in O(1) update time. <i>Algorithmica</i>. 2020;82(4):1057-1080. doi:<a href=\"https://doi.org/10.1007/s00453-019-00630-4\">10.1007/s00453-019-00630-4</a>","short":"S. Bhattacharya, D. Chakrabarty, M.H. Henzinger, Algorithmica 82 (2020) 1057–1080.","apa":"Bhattacharya, S., Chakrabarty, D., &#38; Henzinger, M. H. (2020). Deterministic dynamic matching in O(1) update time. <i>Algorithmica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00453-019-00630-4\">https://doi.org/10.1007/s00453-019-00630-4</a>","chicago":"Bhattacharya, Sayan, Deeparnab Chakrabarty, and Monika H Henzinger. “Deterministic Dynamic Matching in O(1) Update Time.” <i>Algorithmica</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00453-019-00630-4\">https://doi.org/10.1007/s00453-019-00630-4</a>.","ista":"Bhattacharya S, Chakrabarty D, Henzinger MH. 2020. Deterministic dynamic matching in O(1) update time. Algorithmica. 82(4), 1057–1080."},"date_created":"2022-07-27T14:31:06Z","month":"04"}