{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:28:07Z","timestamp":1750307287159,"version":"3.41.0"},"reference-count":25,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2011,7,1]],"date-time":"2011-07-01T00:00:00Z","timestamp":1309478400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000143","name":"Division of Computing and Communication Foundations","doi-asserted-by":"publisher","award":["CCF-0133096"],"award-info":[{"award-number":["CCF-0133096"]}],"id":[{"id":"10.13039\/100000143","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001742","name":"United States-Israel Binational Science Foundation","doi-asserted-by":"publisher","award":["2002246"],"award-info":[{"award-number":["2002246"]}],"id":[{"id":"10.13039\/501100001742","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-04-1-047"],"award-info":[{"award-number":["N00014-04-1-047"]}],"id":[{"id":"10.13039\/100000006","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":[[2011,7]]},"abstract":"<jats:p>\n            We present a deterministic logspace algorithm for solving S-T Connectivity on directed graphs if: (i) we are given a stationary distribution of the random walk on the graph in which both of the input vertices\n            <jats:italic>s<\/jats:italic>\n            and\n            <jats:italic>t<\/jats:italic>\n            have nonnegligible probability mass and (ii) the random walk which starts at the source vertex\n            <jats:italic>s<\/jats:italic>\n            has polynomial mixing time. This result generalizes the recent deterministic logspace algorithm for S-T Connectivity on undirected graphs [Reingold, 2008]. It identifies knowledge of the stationary distribution as the gap between the S-T Connectivity problems we know how to solve in logspace (\n            <jats:bold>L<\/jats:bold>\n            ) and those that capture all of randomized logspace (\n            <jats:bold>RL<\/jats:bold>\n            ).\n          <\/jats:p>","DOI":"10.1145\/1978782.1978785","type":"journal-article","created":{"date-parts":[[2011,7,21]],"date-time":"2011-07-21T13:27:09Z","timestamp":1311254829000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["S-T connectivity on digraphs with a known stationary distribution"],"prefix":"10.1145","volume":"7","author":[{"given":"Kai-Min","family":"Chung","sequence":"first","affiliation":[{"name":"Harvard University, Oxford, Cambridge, MA"}]},{"given":"Omer","family":"Reingold","sequence":"additional","affiliation":[{"name":"Microsoft Research SVC, Mountain View, CA"}]},{"given":"Salil","family":"Vadhan","sequence":"additional","affiliation":[{"name":"Harvard University, Oxford, Cambridge, MA"}]}],"member":"320","published-online":{"date-parts":[[2011,7,15]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Aldous D. and Fill J. 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