{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,13]],"date-time":"2026-09-13T12:53:23Z","timestamp":1789304003768,"version":"build-2803163510"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["340506"],"award-info":[{"award-number":["340506"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["317532"],"award-info":[{"award-number":["317532"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003407","name":"Ministero dell'Istruzione, dell'Universit\u00c3\u00a0 e della Ricerca","doi-asserted-by":"publisher","award":["AMANDA"],"award-info":[{"award-number":["AMANDA"]}],"id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>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 $o(\\sqrt{m})$ time per update. In particular, for minimum vertex cover, we provide deterministic data structures for maintaining a $(2+\\epsilon)$ approximation in $O(\\log n\/\\epsilon^2)$ amortized time per update. For maximum matching, we show how to maintain a $(3+\\epsilon)$ approximation in $O(\\min(\\sqrt{n}\/\\epsilon, m^{1\/3}\/\\epsilon^2)$ amortized time per update and a $(4+\\epsilon)$ approximation in $O(m^{1\/3}\/\\epsilon^2)$ 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].<\/jats:p>","DOI":"10.1137\/140998925","type":"journal-article","created":{"date-parts":[[2018,6,20]],"date-time":"2018-06-20T13:47:32Z","timestamp":1529502452000},"page":"859-887","source":"Crossref","is-referenced-by-count":24,"title":["Deterministic Fully Dynamic Data Structures for Vertex Cover and Matching"],"prefix":"10.1137","volume":"47","author":[{"given":"Sayan","family":"Bhattacharya","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Monika","family":"Henzinger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giuseppe F.","family":"Italiano","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,6,20]]},"reference":[{"key":"atypb1","first-page":"434","author":"Abboud A.","year":"2014","journal-title":"IEEE Computer Society"},{"key":"atypb2","first-page":"383","author":"Baswana S.","year":"2011","journal-title":"IEEE Computer Society"},{"key":"atypb3","first-page":"167","author":"Bernstein A.","year":"2015","journal-title":"Springer"},{"key":"atypb4","first-page":"692","author":"Bernstein A.","year":"2016","journal-title":"SIAM"},{"key":"atypb5","first-page":"86","author":"Bhattacharya S.","year":"2017","journal-title":"Springer"},{"key":"atypb6","first-page":"398","author":"Bhattacharya S.","year":"2016","journal-title":"ACM"},{"key":"atypb7","first-page":"470","author":"Bhattacharya S.","year":"2017","journal-title":"SIAM"},{"key":"atypb8","first-page":"673","author":"Duan R.","year":"2010","journal-title":"IEEE Computer Society"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1145\/2529989"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1145\/115234.115366"},{"key":"atypb11","first-page":"537","author":"Gupta A.","year":"2017","journal-title":"ACM"},{"key":"atypb12","first-page":"548","author":"Gupta M.","year":"2013","journal-title":"IEEE Computer Society"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/0202019"},{"key":"atypb14","first-page":"99","author":"Ivkovic Z.","year":"1993","journal-title":"Springer"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2007.06.019"},{"key":"atypb16","unstructured":"L. Lov\u00e1sz and M. D. Plummer,\n                      Matching Theory\n                      , Akad\u00e9miai Kiad\u00f3, Budapest, 1986. 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