{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T21:20:29Z","timestamp":1775078429417,"version":"3.50.1"},"reference-count":19,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2011,3,24]],"date-time":"2011-03-24T00:00:00Z","timestamp":1300924800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[2011,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For various random constraint satisfaction problems there is a significant gap between the largest constraint density for which solutions exist and the largest density for which any polynomial time algorithm is known to find solutions. Examples of this phenomenon include random <jats:italic>k<\/jats:italic>\u2010SAT, random graph coloring, and a number of other random constraint satisfaction problems. To understand this gap, we study the structure of the solution space of random <jats:italic>k<\/jats:italic>\u2010SAT (i.e., the set of all satisfying assignments viewed as a subgraph of the Hamming cube). We prove that for densities well below the satisfiability threshold, the solution space decomposes into an exponential number of connected components and give quantitative bounds for the diameter, volume, and number.\u00a9 2010 Wiley Periodicals, Inc. Random Struct. Alg., 38, 251\u2013268, 2011<\/jats:p>","DOI":"10.1002\/rsa.20323","type":"journal-article","created":{"date-parts":[[2010,3,29]],"date-time":"2010-03-29T15:25:48Z","timestamp":1269876348000},"page":"251-268","source":"Crossref","is-referenced-by-count":67,"title":["On the solution\u2010space geometry of random constraint satisfaction problems"],"prefix":"10.1002","volume":"38","author":[{"given":"Dimitris","family":"Achlioptas","sequence":"first","affiliation":[]},{"given":"Amin","family":"Coja\u2010Oghlan","sequence":"additional","affiliation":[]},{"given":"Federico","family":"Ricci\u2010Tersenghi","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2011,3,24]]},"reference":[{"key":"e_1_2_8_2_2","first-page":"793","volume-title":"In Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS'08)","author":"Achlioptas D.","year":"2008"},{"key":"e_1_2_8_3_2","first-page":"126","volume-title":"In Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS'02)","author":"Achlioptas D.","year":"2002"},{"key":"e_1_2_8_4_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature03602"},{"key":"e_1_2_8_5_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-04-00464-3"},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/070680382"},{"key":"e_1_2_8_7_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.78.040101"},{"key":"e_1_2_8_8_2","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1997.0867"},{"key":"e_1_2_8_9_2","article-title":"Typical random 3\u2010SAT formulae and the satisfiablity threshold","volume":"10","author":"Dubois O.","year":"2003","journal-title":"Electro Colloq Comput Complex"},{"key":"e_1_2_8_10_2","first-page":"35","article-title":"Supersaturated graphs and hypergraphs","volume":"7","author":"Erd&0151;s P.","year":"1987","journal-title":"Combinatorica"},{"key":"e_1_2_8_11_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-99-00305-7"},{"key":"e_1_2_8_12_2","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20042"},{"key":"e_1_2_8_13_2","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1996.0016"},{"key":"e_1_2_8_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1571-0653(04)00462-7"},{"key":"e_1_2_8_15_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2418(199805)12:3<253::AID-RSA3>3.0.CO;2-U"},{"key":"e_1_2_8_16_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0703685104"},{"key":"e_1_2_8_17_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.94.197205"},{"key":"e_1_2_8_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2008.01.005"},{"key":"e_1_2_8_19_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1073287"},{"key":"e_1_2_8_20_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100010112"}],"container-title":["Random Structures &amp; Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.20323","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.20323","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T05:12:01Z","timestamp":1698729121000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.20323"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3,24]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,5]]}},"alternative-id":["10.1002\/rsa.20323"],"URL":"https:\/\/doi.org\/10.1002\/rsa.20323","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3,24]]}}}