{"scopus_import":"1","quality_controlled":"1","title":"Deterministic fully dynamic data structures for vertex cover and matching","main_file_link":[{"url":"https://arxiv.org/abs/1412.1318","open_access":"1"}],"oa_version":"Preprint","issue":"3","language":[{"iso":"eng"}],"intvolume":"        47","day":"01","year":"2018","article_type":"original","publisher":"Society for Industrial & Applied Mathematics","date_published":"2018-05-01T00:00:00Z","related_material":{"record":[{"id":"11875","status":"public","relation":"earlier_version"}]},"_id":"11890","doi":"10.1137/140998925","author":[{"first_name":"Sayan","full_name":"Bhattacharya, Sayan","last_name":"Bhattacharya"},{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","first_name":"Monika H"},{"last_name":"Italiano","first_name":"Giuseppe F.","full_name":"Italiano, Giuseppe F."}],"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]."}],"publication_status":"published","publication":"SIAM Journal on Computing","extern":"1","type":"journal_article","date_updated":"2023-02-21T16:31:30Z","volume":47,"publication_identifier":{"eissn":["1095-7111"],"issn":["0097-5397"]},"external_id":{"arxiv":["1412.1318"]},"status":"public","page":"859-887","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","month":"05","date_created":"2022-08-17T08:21:23Z","citation":{"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>","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.","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.","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>","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>.","short":"S. Bhattacharya, M.H. Henzinger, G.F. Italiano, SIAM Journal on Computing 47 (2018) 859–887."}}