{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,19]],"date-time":"2026-10-19T23:53:50Z","timestamp":1792454030293,"version":"4.5.0"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>A typical approach to estimate an unknown quantity $\\mu$ is to design an experiment that produces a random variable Z, distributed in [0,1] with E[Z]=\\mu$, run this experiment independently a number of times, and use the average of the outcomes as the estimate. In this paper, we consider the case when no a priori information about Z is known except that is distributed in [0,1]. We describe an approximation algorithm ${\\cal A}{\\cal A}$ which, given $\\epsilon$ and $\\delta$, when running independent experiments with respect to any Z, produces an estimate that is within a factor $1+\\epsilon$ of $\\mu$ with probability at least $1-\\delta$. We prove that the expected number of experiments run by ${\\cal A}{\\cal A}$ (which depends on Z) is optimal to within a constant factor {for every} Z.<\/jats:p>","DOI":"10.1137\/s0097539797315306","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1484-1496","source":"Crossref","is-referenced-by-count":181,"title":["An Optimal Algorithm for Monte Carlo Estimation"],"prefix":"10.1137","volume":"29","author":[{"given":"Paul","family":"Dagum","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard","family":"Karp","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Luby","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sheldon","family":"Ross","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,27]]},"reference":[{"key":"#cr-split#-R1.1","doi-asserted-by":"crossref","unstructured":"A. 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Vazirani,\n                      Polytopes, permanents and graphs with large factors\n                      , in Proceedings of the 29th IEEE Symposium on Foundations of Computer Science, White Plains, NY, 1988, pp. 412\u2013421.","DOI":"10.1109\/SFCS.1988.21957"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(92)90234-7"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/S0004-3702(97)00013-1"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1145\/102782.102783"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548300000675"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01294460"},{"key":"R10","doi-asserted-by":"crossref","unstructured":"M. Jerrum and A. Sinclair,\n                      Conductance and the rapid mixing property for Markov chains: The approximation of the permanent resolved\n                      , in Proceedings of the 20th IEEE Symposium on the Theory of Computing, Chicago, IL, 1988, pp. 235\u2013243.","DOI":"10.1145\/62212.62234"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/0222066"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(86)90174-X"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"M. Jerrum and U. 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Luby,\n                      Monte Carlo algorithms for enumeration and reliability problems\n                      , in Proceedings of the 24th IEEE Symposium on Foundations of Computer Science, Tucson, AZ, 1983, pp. 56\u201364.","DOI":"10.1109\/SFCS.1983.35"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(89)90038-2"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1993.1014"},{"key":"R19","unstructured":"Milena Mihail, Peter Winkler, On the number of Eulerian orientations of a graph, ACM, New York, 1992, 138\u201314593f:05059"},{"key":"R20","unstructured":"D. Randall and A. Sinclair,\n                      Testable algorithms for selfavoiding walks\n                      , in Proceedings of the 5th ACM\/SIAM Symposium on Discrete Algorithms, 1994, pp. 593\u2013602."},{"key":"R21","doi-asserted-by":"crossref","unstructured":"D. Siegmund,\n                      Sequential Analysis\n                      , Springer\u2010Verlag, New York, 1985.","DOI":"10.1007\/978-1-4757-1862-1"},{"key":"R22","unstructured":"A. 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