{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T05:52:19Z","timestamp":1790488339597,"version":"4.1.0"},"reference-count":21,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":5397,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[1992,1]]},"abstract":"Abstract<\/jats:title>\n \n In a random graph on\n n<\/jats:italic>\n vertices, the maximum clique is likely to be of size very close to 2 lg\n n<\/jats:italic>\n . However, the clique produced by applying the naive \u201cgreedy\u201d heuristic to a random graph is unlikely to have size much exceeding lg\n n<\/jats:italic>\n . The factor of two separating these estimates motivates the search for more effective heuristics. This article analyzes a heuristic search strategy, the\n Metropolis process<\/jats:italic>\n , which is just one step above the greedy one in its level of sophistication. It is shown that the Metropolis process takes super\u2010polynomial time to locate a clique that is only slightly bigger than that produced by the greedy heuristic.\n <\/jats:p>","DOI":"10.1002\/rsa.3240030402","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T14:21:42Z","timestamp":1180189302000},"page":"347-359","source":"Crossref","is-referenced-by-count":193,"title":["Large Cliques Elude the Metropolis Process"],"prefix":"10.1002","volume":"3","author":[{"given":"Mark","family":"Jerrum","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100053056"},{"key":"e_1_2_1_3_2","volume-title":"Random Graphs","author":"Bollob\u00e1s B.","year":"1985"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"R. B.Boppana Eigenvalues and graph bisection: An average\u2010case analysis (extended abstract) Proceedings of the 28th IEEE Symposium on Foundations of Computer Science 1987 pp.280\u2013285.","DOI":"10.1109\/SFCS.1987.22"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579448"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(89)90001-1"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","unstructured":"M.Dyer A.Frieze andR.Kannan A random polynomial time algorithm for approximating the volume of convex bodies Proceedings of the 21st ACM Symposium on Theory of Computing 1989 pp.375\u2013381.","DOI":"10.1145\/73007.73043"},{"key":"e_1_2_1_8_2","unstructured":"A. M.Frieze A Note on Computing Random Permanents unpublished manuscript (1989)."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100051124"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1137\/0218077"},{"key":"e_1_2_1_11_2","unstructured":"M. R.JerrumandA. J.Sinclair Polynomial\u2010time Approximation Algorithms for the Ising Model Internal Rep. CSR\u20101\u201390 Department of Computer Science University of Edinburgh 1990. (Accepted for publication inSIAM J. Comput.)."},{"key":"e_1_2_1_12_2","volume-title":"Algorithms and Complexity: New Directions and Recent Results","author":"Karp R. M.","year":"1976"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.220.4598.671"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(89)90200-7"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01874388"},{"key":"e_1_2_1_16_2","first-page":"A\u2010382","article-title":"The employee party problem","volume":"19","author":"Matula D. W.","year":"1972","journal-title":"Notices Am. Math. Soc."},{"key":"e_1_2_1_17_2","doi-asserted-by":"crossref","unstructured":"R.Motwani Expanding graphs and the average\u2010case analysis of algorithms for matchings and related problems Proceedings of the 21st ACM Symposium on Theory of Computing 1989 pp.550\u2013561.","DOI":"10.1145\/73007.73060"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100060205"},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(91)90037-I"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1145\/42282.46160"},{"key":"e_1_2_1_21_2","unstructured":"A.Sinclair Randomised Algorithms for Counting and Generating Combinatorial Structures Ph.D. thesis University of Edinburgh 1988."},{"key":"e_1_2_1_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(88)90005-3"}],"container-title":["Random Structures & Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.3240030402","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.3240030402","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T11:00:27Z","timestamp":1698058827000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.3240030402"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,1]]},"references-count":21,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1992,1]]}},"alternative-id":["10.1002\/rsa.3240030402"],"URL":"https:\/\/doi.org\/10.1002\/rsa.3240030402","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,1]]}}}