{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T05:40:35Z","timestamp":1698385235629},"reference-count":18,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4058,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[1995,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study the tail distribution of supercritical branching processes for which the number of offspring of an element is bounded. Given a supercritical branching process {<jats:italic>Z<jats:sub>n<\/jats:sub><\/jats:italic>}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-stack-1.gif\" xlink:title=\"urn:x-wiley:10429832:media:RSA3240070202:tex2gif-stack-1\" \/> with a bounded offspring distribution, we derive a tight bound, decaying super\u2010exponentially fast as <jats:italic>c<\/jats:italic> increases, on the probability Pr[<jats:italic>Z<jats:sub>n<\/jats:sub><\/jats:italic> &gt; <jats:italic>cE<\/jats:italic>(<jats:italic>Z<jats:sub>n<\/jats:sub><\/jats:italic>)], and a similar bound on the probability Pr[<jats:italic>Z<jats:sub>n<\/jats:sub><\/jats:italic> \u2264 <jats:italic>E(Z<jats:sub>n<\/jats:sub>)\/c<\/jats:italic>] under the assumption that each element generates at least two offspring. As an application, we observe that the execution of a canonical algorithm for evaluating uniform AND\/OR trees in certain probabilistic models can be viewed as a two\u2010type supercritical branching process with bounded offspring, and show that the execution time of this algorithm is likely to concentrate around its expectation, with a standard deviation of the same order as the expectation.<\/jats:p>","DOI":"10.1002\/rsa.3240070202","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T18:48:06Z","timestamp":1180205286000},"page":"97-116","source":"Crossref","is-referenced-by-count":10,"title":["Bounded branching process and and\/or tree evaluation"],"prefix":"10.1002","volume":"7","author":[{"given":"Richard M.","family":"Karp","sequence":"first","affiliation":[]},{"given":"Yanjun","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1177004971"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65371-1"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0004-3702(78)80011-3"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/1427790"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2307\/3214158"},{"key":"e_1_2_1_7_2","volume-title":"Stochastic Process","author":"Doob J. 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H.","year":"1990"},{"key":"e_1_2_1_15_2","volume-title":"Heuristics","author":"Pearl J.","year":"1984"},{"key":"e_1_2_1_16_2","doi-asserted-by":"crossref","unstructured":"M.SaksandA.Wigderson Probabilistic boolean decision trees and complexity of evaluating game trees 27th Annual Symposium on Foundations of Computer Science 1986 pp.29\u201338.","DOI":"10.1109\/SFCS.1986.44"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970074"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1145\/2402.322383"},{"key":"e_1_2_1_19_2","unstructured":"A.Vidyashankar Large deviation rates for branching processes in fixed and random environments Ph.D. thesis Department of Statistics Iowa State University Ames 1994."}],"container-title":["Random Structures &amp; Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.3240070202","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.3240070202","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T02:50:41Z","timestamp":1698288641000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.3240070202"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,9]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1995,9]]}},"alternative-id":["10.1002\/rsa.3240070202"],"URL":"https:\/\/doi.org\/10.1002\/rsa.3240070202","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,9]]}}}