{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T14:33:48Z","timestamp":1774190028563,"version":"3.50.1"},"reference-count":30,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2011,5,1]],"date-time":"2011-05-01T00:00:00Z","timestamp":1304208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["J. ACM"],"published-print":{"date-parts":[[2011,5]]},"abstract":"<jats:p>\n            This article focuses on computations on large graphs (e.g., the web-graph) where the edges of the graph are presented as a stream. The objective in the streaming model is to use small amount of memory (preferably sub-linear in the number of nodes\n            <jats:italic>n<\/jats:italic>\n            ) and a smaller number of passes.\n          <\/jats:p>\n          <jats:p>\n            In the streaming model, we show how to perform several graph computations including estimating the probability distribution after a random walk of length\n            <jats:italic>l<\/jats:italic>\n            , the mixing time\n            <jats:italic>M<\/jats:italic>\n            , and other related quantities such as the conductance of the graph. By applying our algorithm for computing probability distribution on the web-graph, we can estimate the\n            <jats:italic>PageRank<\/jats:italic>\n            <jats:italic>p<\/jats:italic>\n            of any node up to an additive error of \u221a\u03b5\n            <jats:italic>p<\/jats:italic>\n            +\u03b5 in\n            <jats:italic>\u00d5<\/jats:italic>\n            (\u221a\n            <jats:italic>M<\/jats:italic>\n            \/\u03b1) passes and\n            <jats:italic>\u00d5<\/jats:italic>\n            (min(\n            <jats:italic>n<\/jats:italic>\n            \u03b1+1\/\u03b5\u221a\n            <jats:italic>M<\/jats:italic>\n            \/\u03b1+(1\/\u03b5)\n            <jats:italic>M<\/jats:italic>\n            \u03b1, \u03b1\n            <jats:italic>n<\/jats:italic>\n            \u221a\n            <jats:italic>M<\/jats:italic>\n            \u03b1 + (1\/\u03b5)\u221a\n            <jats:italic>M<\/jats:italic>\n            \/\u03b1)) space, for any \u03b1 \u2208 (0,1]. Specifically, for \u03b5 =\n            <jats:italic>M<\/jats:italic>\n            \/\n            <jats:italic>n<\/jats:italic>\n            , \u03b1 =\n            <jats:italic>M<\/jats:italic>\n            <jats:sup>\u22121\/2<\/jats:sup>\n            , we can compute the approximate PageRank values in \u00d5(\n            <jats:italic>nM<\/jats:italic>\n            <jats:sup>\u22121\/4<\/jats:sup>\n            ) space and \u00d5(\n            <jats:italic>M<\/jats:italic>\n            <jats:sup>3\/4<\/jats:sup>\n            ) passes. In comparison, a standard implementation of the PageRank algorithm will take\n            <jats:italic>O(n)<\/jats:italic>\n            space and\n            <jats:italic>O(M)<\/jats:italic>\n            passes. We also give an approach to approximate the PageRank values in just \u00d5(1) passes although this requires \u00d5(\n            <jats:italic>nM<\/jats:italic>\n            ) space.\n          <\/jats:p>","DOI":"10.1145\/1970392.1970397","type":"journal-article","created":{"date-parts":[[2011,6,6]],"date-time":"2011-06-06T11:51:38Z","timestamp":1307361098000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":51,"title":["Estimating PageRank on graph streams"],"prefix":"10.1145","volume":"58","author":[{"given":"Atish Das","family":"Sarma","sequence":"first","affiliation":[{"name":"Georgia Institute of Technology, Mountain View, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sreenivas","family":"Gollapudi","sequence":"additional","affiliation":[{"name":"Microsoft Research, Mountain View, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rina","family":"Panigrahy","sequence":"additional","affiliation":[{"name":"Microsoft Research"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2011,6,9]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1997.1545"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2006.44"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/258533.258593"},{"key":"e_1_2_1_4_1","volume-title":"Proceedings of the ACM-SIAM Symposium on Discrete Algorithms. 623--632","author":"Bar-Yossef Z."},{"key":"e_1_2_1_5_1","volume-title":"Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science (FOCS). 442--451","author":"Batu T."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/11841036_16"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.5555\/1109557.1109634"},{"key":"e_1_2_1_8_1","volume-title":"Proceedings of the 7th International Conference on World Wide Web. 107--117","author":"Brin S."},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/1142351.1142388"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1065167.1065201"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.5555\/1109557.1109635"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1997.1471"},{"key":"e_1_2_1_13_1","volume-title":"Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA). 745--754","author":"Feigenbaum J."},{"key":"e_1_2_1_14_1","unstructured":"Feldman J. 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