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Discov. Data"],"published-print":{"date-parts":[[2015,4,13]]},"abstract":"<jats:p>\n                    We design a space-efficient algorithm that approximates the transitivity (global clustering coefficient) and total triangle count with only a single pass through a graph given as a stream of edges. Our procedure is based on the classic probabilistic result,\n                    <jats:italic>the birthday paradox<\/jats:italic>\n                    . When the transitivity is constant and there are more edges than wedges (common properties for social networks), we can prove that our algorithm requires\n                    <jats:italic>O<\/jats:italic>\n                    (\u221a\n                    <jats:italic>n<\/jats:italic>\n                    ) space (\n                    <jats:italic>n<\/jats:italic>\n                    is the number of vertices) to provide accurate estimates. We run a detailed set of experiments on a variety of real graphs and demonstrate that the memory requirement of the algorithm is a tiny fraction of the graph. For example, even for a graph with 200 million edges, our algorithm stores just 40,000 edges to give accurate results. Being a single pass streaming algorithm, our procedure also maintains a real-time estimate of the transitivity\/number of triangles of a graph by storing a minuscule fraction of edges.\n                  <\/jats:p>","DOI":"10.1145\/2700395","type":"journal-article","created":{"date-parts":[[2015,2,18]],"date-time":"2015-02-18T08:24:05Z","timestamp":1424247845000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":36,"title":["A Space-Efficient Streaming Algorithm for Estimating Transitivity and Triangle Counts Using the Birthday Paradox"],"prefix":"10.1145","volume":"9","author":[{"given":"Madhav","family":"Jha","sequence":"first","affiliation":[{"name":"Sandia National Laboratories"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C.","family":"Seshadhri","sequence":"additional","affiliation":[{"name":"Sandia National Laboratories"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ali","family":"Pinar","sequence":"additional","affiliation":[{"name":"Sandia National Laboratories"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2015,2,17]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2623330.2623757"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601438"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2213556.2213560"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/IPDPS.2010.5470440"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2505515.2505545"},{"key":"e_1_2_1_6_1","volume-title":"Proceedings of the KDD Workshop on Large Scale Data Mining.","author":"Avron Haim","year":"2010"},{"key":"e_1_2_1_7_1","volume-title":"Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA\u201902)","author":"Bar-Yossef Ziv"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/1401890.1401898"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1109\/IPDPS.2007.370685"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/1142351.1142388"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1086\/421787"},{"key":"e_1_2_1_13_1","volume-title":"Proceedings of the 9th Annual IEEE\/ACM International Symposium on Code Generation and Optimization (CGO\u201911)","author":"Chakrabarti Dhruva R.","year":"1900"},{"key":"e_1_2_1_14_1","volume-title":"Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA\u201995)","author":"Chiang Yi-Jen","year":"1995"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1137\/0214017"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/2020408.2020513"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCSE.2009.120"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1086\/228943"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/2396761.2398503"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.032093399"},{"key":"e_1_2_1_21_1","volume-title":"An Introduction to Probability Theory and Applications (Vol. I","author":"Feller William","edition":"3"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/1753846.1754097"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/2463676.2463704"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/2487575.2487678"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.5555\/2958119.2958158"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-31585-5_53"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1137\/13090729X"},{"key":"e_1_2_1_28_1","volume-title":"Proceedings of the 7th International Workshop on Algorithms and Models for the Web-Graph. 15--24","author":"Kolountzakis Mihail N.","year":"1800"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2008.07.017"},{"key":"e_1_2_1_30_1","doi-asserted-by":"crossref","unstructured":"Ron Milo ShaiShen-Orr Shalev Itzkovitz Nadav Kashtan David Chklovskii and Uri Alon. 2002. 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