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ACM"],"published-print":{"date-parts":[[2007,7]]},"abstract":"<jats:p>\n            This article provides a new conceptual perspective on\n            <jats:italic>survey propagation<\/jats:italic>\n            , which is an iterative algorithm recently introduced by the statistical physics community that is very effective in solving random\n            <jats:italic>k<\/jats:italic>\n            -SAT problems even with densities close to the satisfiability threshold. We first describe how any SAT formula can be associated with a novel family of Markov random fields (MRFs), parameterized by a real number \u03c1 \u2208 [0, 1]. We then show that applying belief propagation---a well-known \u201cmessage-passing\u201d technique for estimating marginal probabilities---to this family of MRFs recovers a known family of algorithms, ranging from pure survey propagation at one extreme (\u03c1 = 1) to standard belief propagation on the uniform distribution over SAT assignments at the other extreme (\u03c1 = 0). Configurations in these MRFs have a natural interpretation as partial satisfiability assignments, on which a partial order can be defined. We isolate\n            <jats:italic>cores<\/jats:italic>\n            as minimal elements in this partial ordering, which are also fixed points of survey propagation and the only assignments with positive probability in the MRF for \u03c1 = 1. Our experimental results for\n            <jats:italic>k<\/jats:italic>\n            = 3 suggest that solutions of random formulas typically do not possess non-trivial cores. This makes it necessary to study the structure of the space of partial assignments for \u03c1 &lt; 1 and investigate the role of assignments that are very close to being cores. To that end, we investigate the associated lattice structure, and prove a weight-preserving identity that shows how any MRF with \u03c1 &gt; 0 can be viewed as a \u201csmoothed\u201d version of the uniform distribution over satisfying assignments (\u03c1 = 0). Finally, we isolate properties of Gibbs sampling and message-passing algorithms that are typical for an ensemble of\n            <jats:italic>k<\/jats:italic>\n            -SAT problems.\n          <\/jats:p>","DOI":"10.1145\/1255443.1255445","type":"journal-article","created":{"date-parts":[[2007,9,14]],"date-time":"2007-09-14T13:44:55Z","timestamp":1189777495000},"page":"17","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":54,"title":["A new look at survey propagation and its generalizations"],"prefix":"10.1145","volume":"54","author":[{"given":"Elitza","family":"Maneva","sequence":"first","affiliation":[{"name":"University of California---Berkeley, Berkeley, California"}]},{"given":"Elchanan","family":"Mossel","sequence":"additional","affiliation":[{"name":"University of California---Berkeley, Berkeley, California"}]},{"given":"Martin J.","family":"Wainwright","sequence":"additional","affiliation":[{"name":"University of California---Berkeley, Berkeley, California"}]}],"member":"320","published-online":{"date-parts":[[2007,7]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Proceedings of the Symposium on the Foundations of Computer Science. IEEE Computer Society Press","author":"Achiloptas D.","unstructured":"Achiloptas , D. , and Peres , Y . 2003. The threshold for random k-SAT is 2k2log 2&minus;o(k) . In Proceedings of the Symposium on the Foundations of Computer Science. IEEE Computer Society Press , Los Alamitos, CA, 223--231. 10.1145\/780542.780577 Achiloptas, D., and Peres, Y. 2003. The threshold for random k-SAT is 2k2log 2&minus;o(k). In Proceedings of the Symposium on the Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, CA, 223--231. 10.1145\/780542.780577"},{"key":"e_1_2_1_2_1","volume-title":"Proceedings of the Symposium on Theory of Computing. ACM","author":"Achlioptas D.","unstructured":"Achlioptas , D. , and Ricci-Tersenghi , F . 2006. On the solution-space geometry of random constraint satisfaction problems . In Proceedings of the Symposium on Theory of Computing. ACM , New York, 130--139. 10.1145\/1132516.1132537 Achlioptas, D., and Ricci-Tersenghi, F. 2006. 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