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Comput. Theory"],"published-print":{"date-parts":[[2012,11]]},"abstract":"<jats:p>\n            <jats:italic>The Total Influence<\/jats:italic>\n            (\n            <jats:italic>Average Sensitivity<\/jats:italic>\n            ) of a discrete function is one of its fundamental measures. We study the problem of approximating the total influence of a monotone Boolean function, which we denote by\n            <jats:italic>I<\/jats:italic>\n            [\n            <jats:italic>f<\/jats:italic>\n            ]. We present a randomized algorithm that approximates the influence of such functions to within a multiplicative factor of (1 \u00b1\n            <jats:italic>\u03b5<\/jats:italic>\n            ) by performing\n            <jats:italic>O<\/jats:italic>\n            (\u221a\n            <jats:italic>n<\/jats:italic>\n            <jats:italic>I<\/jats:italic>\n            [\n            <jats:italic>f<\/jats:italic>\n            ] poly(1\/\n            <jats:italic>\u03b5<\/jats:italic>\n            )) queries. We also prove a lower bound of\n            <jats:italic>\u03a9<\/jats:italic>\n            (\u221a\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:italic>n<\/jats:italic>\n            \u00b7\n            <jats:italic>I<\/jats:italic>\n            [\n            <jats:italic>f<\/jats:italic>\n            ]) on the query complexity of any constant factor approximation algorithm for this problem (which holds for\n            <jats:italic>I<\/jats:italic>\n            [\n            <jats:italic>f<\/jats:italic>\n            ]=\n            <jats:italic>\u03a9<\/jats:italic>\n            (1)), hence showing that our algorithm is almost optimal in terms of its dependence on\n            <jats:italic>n<\/jats:italic>\n            . For general functions, we give a lower bound of\n            <jats:italic>\u03a9<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            <jats:italic>I<\/jats:italic>\n            [\n            <jats:italic>f<\/jats:italic>\n            ]), which matches the complexity of a simple sampling algorithm.\n          <\/jats:p>","DOI":"10.1145\/2382559.2382562","type":"journal-article","created":{"date-parts":[[2012,12,4]],"date-time":"2012-12-04T20:10:57Z","timestamp":1354651857000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":11,"title":["Approximating the Influence of Monotone Boolean Functions in O(\u221an) Query Complexity"],"prefix":"10.1145","volume":"4","author":[{"given":"Dana","family":"Ron","sequence":"first","affiliation":[{"name":"School of Electrical Engineering at Tel Aviv University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ronitt","family":"Rubinfeld","sequence":"additional","affiliation":[{"name":"CSAIL at MIT, and the Blavatnik School of Computer Science at Tel Aviv University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muli","family":"Safra","sequence":"additional","affiliation":[{"name":"Blavatnik School of Computer Science at Tel Aviv University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alex","family":"Samorodnitsky","sequence":"additional","affiliation":[{"name":"The Institute for Computer Science, Hebrew University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Omri","family":"Weinstein","sequence":"additional","affiliation":[{"name":"Princeton University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2012,11]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1086\/256963"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02698830"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1985.15"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-85363-3_26"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1536414.1536437"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/CCC.2011.31"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(97)00131-2"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/s000390050015"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02808010"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/234533.234564"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/1806689.1806763"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.2307\/1969503"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/509907.509915"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-007-0068-9"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/509907.509977"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2003.11.004"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009809"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548303005832"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-96-03732-X"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/s004930070011"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(76)90079-0"},{"volume-title":"Proceedings of COLT. 179--183","author":"Hancock T.","key":"e_1_2_1_22_1","unstructured":"Hancock , T. and Mansour , Y . 1991. 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