{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T18:51:06Z","timestamp":1791571866757,"version":"4.3.4"},"reference-count":17,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2017,4,30]],"date-time":"2017-04-30T00:00:00Z","timestamp":1493510400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"ISF","award":["1696\/14"],"award-info":[{"award-number":["1696\/14"]}]},{"name":"BSF","award":["2015803"],"award-info":[{"award-number":["2015803"]}]},{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["CCF-1618280 and CCF-1527110"],"award-info":[{"award-number":["CCF-1618280 and CCF-1527110"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2017,4,30]]},"abstract":"<jats:p>\n            A fundamental result by Karger [10] states that for any \u03bb-edge-connected graph with\n            <jats:italic>n<\/jats:italic>\n            nodes, independently sampling each edge with probability\n            <jats:italic>p<\/jats:italic>\n            = \u03a9(log (\n            <jats:italic>n<\/jats:italic>\n            )\/\u03bb) results in a graph that has edge connectivity \u03a9(\u03bb\n            <jats:italic>p<\/jats:italic>\n            ), with high probability. This article proves the analogous result for vertex connectivity, when either vertices or edges are sampled. We show that for any\n            <jats:italic>k<\/jats:italic>\n            -vertex-connected graph\n            <jats:italic>G<\/jats:italic>\n            with\n            <jats:italic>n<\/jats:italic>\n            nodes, if each node is independently sampled with probability\n            <jats:italic>p<\/jats:italic>\n            =\u03a9(\u221alog(\n            <jats:italic>n<\/jats:italic>\n            )\/\n            <jats:italic>k<\/jats:italic>\n            ), then the subgraph induced by the sampled nodes has vertex connectivity \u03a9(\n            <jats:italic>kp<\/jats:italic>\n            <jats:sup>2<\/jats:sup>\n            ), with high probability. If edges are sampled with probability\n            <jats:italic>p<\/jats:italic>\n            = \u03a9(log (\n            <jats:italic>n<\/jats:italic>\n            )\/\n            <jats:italic>k<\/jats:italic>\n            ), then the sampled subgraph has vertex connectivity \u03a9(\n            <jats:italic>kp<\/jats:italic>\n            ), with high probability. Both bounds are existentially optimal.\n          <\/jats:p>","DOI":"10.1145\/3086465","type":"journal-article","created":{"date-parts":[[2017,5,31]],"date-time":"2017-05-31T19:32:40Z","timestamp":1496259160000},"page":"1-26","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["Tight Bounds on Vertex Connectivity Under Sampling"],"prefix":"10.1145","volume":"13","author":[{"given":"Keren","family":"Censor-Hillel","sequence":"first","affiliation":[{"name":"Technion, Haifa, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohsen","family":"Ghaffari","sequence":"additional","affiliation":[{"name":"MIT"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"George","family":"Giakkoupis","sequence":"additional","affiliation":[{"name":"INRIA, Rennes Cedex, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bernhard","family":"Haeupler","sequence":"additional","affiliation":[{"name":"Carnegie Mellon University, Pittsburgh PA, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fabian","family":"Kuhn","sequence":"additional","affiliation":[{"name":"University of Freiburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2017,5,29]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Discrete Probability and Algorithms","author":"Alon Noga"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/237814.237827"},{"key":"e_1_2_1_3_1","volume-title":"Random Graphs","author":"Bollob\u00e1s B\u00e9la"},{"key":"e_1_2_1_4_1","doi-asserted-by":"crossref","unstructured":"B\u00e9la Bollob\u00e1s and Oliver Riordan. 2006. 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