{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T02:22:56Z","timestamp":1772936576962,"version":"3.50.1"},"reference-count":66,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1815316"],"award-info":[{"award-number":["CCF-1815316"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-2221980"],"award-info":[{"award-number":["CCF-2221980"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-2238138"],"award-info":[{"award-number":["CCF-2238138"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[2026,4,30]]},"DOI":"10.1137\/23m1564845","type":"journal-article","created":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T08:09:26Z","timestamp":1772438966000},"page":"280-306","source":"Crossref","is-referenced-by-count":0,"title":["Space Complexity of Vertex Connectivity Oracles"],"prefix":"10.1137","volume":"55","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0495-3904","authenticated-orcid":true,"given":"Seth","family":"Pettie","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, University of Michigan, Ann Arbor, MI 48109 USA."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8386-7168","authenticated-orcid":true,"given":"Thatchaphol","family":"Saranurak","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, University of Michigan, Ann Arbor, MI 48109 USA."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5696-5678","authenticated-orcid":true,"given":"Longhui","family":"Yin","sequence":"additional","affiliation":[{"name":"Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100190, People\u2019s Republic of China."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"351","published-online":{"date-parts":[[2026,3,2]]},"reference":[{"key":"ref1","series-title":"Leibniz International Proceedings in Informatics (LIPIcs) 132","first-page":"7:1","volume-title":"46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)","author":"Abboud A.","year":"2019"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS54457.2022.00088"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611978315.30"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539792236730"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1995.492466"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-85221-6_3"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/10719839_9"},{"key":"ref8","series-title":"Cambridge Studies in Advanced Mathematics 73","volume-title":"Random Graphs","author":"Bollob\u00e1s B.","year":"2011","edition":"2"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01840366"},{"key":"ref10","unstructured":"C. Chekuri, Some Open Problems in Element-Connectivity, http:\/\/chekuri.cs.illinois.edu\/papers\/elem-connectivity-open-probs.pdf, 2015."},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/120882147"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-48350-3_27"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1145\/3728631"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1007\/BF02115755"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/110844970"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.4086\/toc.2012.v008a018"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1145\/167088.167152"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02927-1_29"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1007\/BF01961541"},{"key":"ref20","first-page":"290","volume-title":"Studies in Discrete Optimization","author":"Dinic E. A.","year":"1976"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1145\/225058.225268"},{"key":"ref22","unstructured":"Y. Dinitz and Z. Nutov, A 2-Level Cactus Tree Model for the System of Minimum and Minimum\\(+1\\) Edge Cuts of a Graph and Its Incremental Maintenance. Part I: The Odd Case, manuscript, 1999."},{"key":"ref23","unstructured":"Y. Dinitz and Z. Nutov, A 2-Level Cactus Tree Model for the System of Minimum and Minimum\\(+1\\) Edge Cuts of a Graph and Its Incremental Maintenance. Part II: The Even Case, manuscript, 1999."},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1145\/195058.195442"},{"key":"ref25","unstructured":"Y. Dinitz and A. Vainshtein, Locally orientable graphs, cell structures, and a new algorithm for the incremental maintenance of connectivity carcasses, in SODA95: Conference on Discrete Algorithms, SIAM, Philadelphia, 1995, pp. 302\u2013311, http:\/\/dl.acm.org\/citation.cfm?id=313651.313711."},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539797330045"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(98)00023-1"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-015-9991-z"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611975994.126"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190170302"},{"key":"ref31","volume-title":"Introduction to Random Graphs","author":"Frieze A.","year":"2016"},{"key":"ref32","series-title":"Leibniz International Proceedings in Informatics (LIPIcs)\u00a0168","first-page":"57:1","volume-title":"47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)","author":"Gawrychowski P.","year":"2020"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611976496.8"},{"key":"ref34","first-page":"9:1","volume":"13","author":"Georgiadis L.","year":"2016","journal-title":"ACM Trans. Algorithms"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2018.02.007"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1137\/0109047"},{"key":"ref37","unstructured":"D. Gusfield and D. Naor, Efficient algorithms for generalized cut trees, in SODA \u201990: Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 1990, pp. 422\u2013433,\u00a0http:\/\/dl.acm.org\/citation.cfm?id=320176.320228."},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230210503"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1007\/BF01908632"},{"key":"ref40","unstructured":"R. Hariharan, T. Kavitha, and D. Panigrahi, Efficient algorithms for computing all low \\(s\\)-\\(t\\) edge connectivities and related problems, in SODA \u201907: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 2007, pp. 127\u2013136, http:\/\/dl.acm.org\/citation.cfm?id=1283383.1283398."},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2006.08.012"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1145\/2746539.2746609"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-10631-6_32"},{"key":"ref44","volume-title":"Integer Programming and Network Flows","author":"Hu T. C.","year":"1969"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2011.10.001"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1016\/S0196-6774(02)00222-5"},{"key":"ref47","first-page":"793","volume-title":"Proceedings of the 32nd Annual Symposium on Foundations of Computer Science","author":"Kanevsky A.","year":"1991"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1145\/331605.331608"},{"key":"ref49","doi-asserted-by":"crossref","unstructured":"D. R. Karger and D. Panigrahi, A near-linear time algorithm for constructing a cactus representation of minimum cuts, in SODA \u201909: Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 2009, pp. 246\u2013255, http:\/\/dl.acm.org\/citation.cfm?id=1496770.1496798.","DOI":"10.1137\/1.9781611973068.28"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539703433912"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974331.ch89"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1145\/1721837.1721855"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1145\/3406325.3451088"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1145\/3406325.3451112"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1145\/3744737"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.4064\/fm-10-1-96-115"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1145\/3357713.3384334"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1007\/BF01758778"},{"key":"ref59","series-title":"Leibniz International Proceedings in Informatics (LIPIcs) 244","first-page":"82:1","volume-title":"in 30th Annual European Symposium on Algorithms (ESA 2022)","author":"Nutov Z.","year":"2022"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-006-0014-1"},{"key":"ref61","series-title":"Leibniz International Proceedings in Informatics (LIPIcs)\u00a0198","first-page":"105:1","volume-title":"48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)","author":"Pettie S.","year":"2021"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1007\/BF01581031"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611976496.9"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1137\/0208019"},{"key":"ref65","series-title":"Algorithms and Combinatorics 24","volume-title":"Combinatorial Optimization: Polyhedra and Efficiency","author":"Schrijver A.","year":"2003"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1145\/3406325.3451108"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T08:09:38Z","timestamp":1772870978000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M1564845"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,2]]},"references-count":66,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,4,30]]}},"alternative-id":["10.1137\/23M1564845"],"URL":"https:\/\/doi.org\/10.1137\/23m1564845","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,2]]}}}