{"publication_identifier":{"issn":["0097-5397"],"eissn":["1095-7111"]},"doi":"10.1137/140998925","_id":"11890","title":"Deterministic fully dynamic data structures for vertex cover and matching","month":"05","issue":"3","oa_version":"Preprint","citation":{"ama":"Bhattacharya S, Henzinger MH, Italiano GF. Deterministic fully dynamic data structures for vertex cover and matching. <i>SIAM Journal on Computing</i>. 2018;47(3):859-887. doi:<a href=\"https://doi.org/10.1137/140998925\">10.1137/140998925</a>","ista":"Bhattacharya S, Henzinger MH, Italiano GF. 2018. Deterministic fully dynamic data structures for vertex cover and matching. SIAM Journal on Computing. 47(3), 859–887.","mla":"Bhattacharya, Sayan, et al. “Deterministic Fully Dynamic Data Structures for Vertex Cover and Matching.” <i>SIAM Journal on Computing</i>, vol. 47, no. 3, Society for Industrial &#38; Applied Mathematics, 2018, pp. 859–87, doi:<a href=\"https://doi.org/10.1137/140998925\">10.1137/140998925</a>.","chicago":"Bhattacharya, Sayan, Monika H Henzinger, and Giuseppe F. Italiano. “Deterministic Fully Dynamic Data Structures for Vertex Cover and Matching.” <i>SIAM Journal on Computing</i>. Society for Industrial &#38; Applied Mathematics, 2018. <a href=\"https://doi.org/10.1137/140998925\">https://doi.org/10.1137/140998925</a>.","ieee":"S. Bhattacharya, M. H. Henzinger, and G. F. Italiano, “Deterministic fully dynamic data structures for vertex cover and matching,” <i>SIAM Journal on Computing</i>, vol. 47, no. 3. Society for Industrial &#38; Applied Mathematics, pp. 859–887, 2018.","short":"S. Bhattacharya, M.H. Henzinger, G.F. Italiano, SIAM Journal on Computing 47 (2018) 859–887.","apa":"Bhattacharya, S., Henzinger, M. H., &#38; Italiano, G. F. (2018). Deterministic fully dynamic data structures for vertex cover and matching. <i>SIAM Journal on Computing</i>. Society for Industrial &#38; Applied Mathematics. <a href=\"https://doi.org/10.1137/140998925\">https://doi.org/10.1137/140998925</a>"},"type":"journal_article","oa":1,"scopus_import":"1","publisher":"Society for Industrial & Applied Mathematics","publication_status":"published","language":[{"iso":"eng"}],"author":[{"last_name":"Bhattacharya","full_name":"Bhattacharya, Sayan","first_name":"Sayan"},{"last_name":"Henzinger","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","first_name":"Monika H","full_name":"Henzinger, Monika H"},{"full_name":"Italiano, Giuseppe F.","first_name":"Giuseppe F.","last_name":"Italiano"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"859-887","publication":"SIAM Journal on Computing","date_created":"2022-08-17T08:21:23Z","year":"2018","date_published":"2018-05-01T00:00:00Z","article_processing_charge":"No","external_id":{"arxiv":["1412.1318"]},"article_type":"original","volume":47,"extern":"1","related_material":{"record":[{"status":"public","id":"11875","relation":"earlier_version"}]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1412.1318"}],"date_updated":"2023-02-21T16:31:30Z","intvolume":"        47","status":"public","abstract":[{"lang":"eng","text":"We present the first deterministic data structures for maintaining approximate minimum vertex cover and maximum matching in a fully dynamic graph 𝐺=(𝑉,𝐸), with |𝑉|=𝑛 and |𝐸|=𝑚, in 𝑜(𝑚‾‾√) time per update. In particular, for minimum vertex cover, we provide deterministic data structures for maintaining a (2+𝜖) approximation in 𝑂(log𝑛/𝜖2) amortized time per update. For maximum matching, we show how to maintain a (3+𝜖) approximation in 𝑂(min(𝑛√/𝜖,𝑚1/3/𝜖2) amortized time per update and a (4+𝜖) approximation in 𝑂(𝑚1/3/𝜖2) worst-case time per update. Our data structure for fully dynamic minimum vertex cover is essentially near-optimal and settles an open problem by Onak and Rubinfeld [in 42nd ACM Symposium on Theory of Computing, Cambridge, MA, ACM, 2010, pp. 457--464]."}],"day":"01","quality_controlled":"1"}