{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T18:35:30Z","timestamp":1725561330933},"publisher-location":"Berlin, Heidelberg","reference-count":23,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540208518"},{"type":"electronic","value":"9783540246053"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2004]]},"DOI":"10.1007\/978-3-540-24605-3_38","type":"book-chapter","created":{"date-parts":[[2010,7,29]],"date-time":"2010-07-29T04:50:35Z","timestamp":1280379035000},"page":"519-528","source":"Crossref","is-referenced-by-count":7,"title":["Survey and Belief Propagation on Random K-SAT"],"prefix":"10.1007","author":[{"given":"Alfredo","family":"Braunstein","sequence":"first","affiliation":[]},{"given":"Riccardo","family":"Zecchina","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"38_CR1","doi-asserted-by":"crossref","unstructured":"M\u00e9zard, M., Zecchina, R.: Random K-satisfiability: from an analytic solution to a new efficient algorithm. 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Theory and Related Fields"},{"key":"38_CR10","unstructured":"The cavity and the replica methods deal with average quantities over some probability distribution of problem instances (e.g. average fraction of violated clauses in random K-SAT problems). See ref. Complex Systems: a Physicist\u2019s View, G. Parisi (2002), cond-mat\/0205297 for a recent review. In ref. [1] it was realized that quite in general the cavity approach could be brought down to the level of single problem instances thus revealing the algorithmic potentialities of the formalism. As discussed in this paper, a simple version of survey propagation was already known to Gallager since 1963 and used in practice as decoding algorithm in Low Density Parity Check codes and Turbo Codes."},{"issue":"1","key":"38_CR11","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s00220-002-0699-y","volume":"230","author":"F. 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Pearl","year":"1988","unstructured":"Pearl, J.: Probabilistic Reasoning in Intelligent Systems, 2nd edn. Morgan Kaufmann, San Francisco (1988)","edition":"2"},{"key":"#cr-split#-38_CR15.1","doi-asserted-by":"crossref","unstructured":"Over the n-dimensional hypercube, we say that two vertices are connected if they represent solutions at Hamming distances one. We define a cluster as a connected component over the whole hypercube. SP looks at clusters with a finite fraction of backbone variables [17,1]. Exact enumerations on small random formulas indeed confirm the onset of clustering below \u03b1c already for rather small values of n (A. Braunstein, V. Napolano, R. Zecchina, in preparation, 2003). Rigorous results about clustering phenomenon taking place in random K-XOR-SAT can be found in: S. Cocco, O. Dubois,J. Mandler, R. Monasson, Rigorous decimation-based construction of ground pure states for spin glass models on random lattices, Phys. Rev. Lett. 90, 047205 (2003): Mezard, M., Ricci-Tersenghi, F., Zecchina, R.: Two solutions to diluted p-spin models and XORSAT problems J. Stat. Phys. 111, 505 (2003);","DOI":"10.1023\/A:1022886412117"},{"key":"#cr-split#-38_CR15.2","unstructured":"We mention that for random 3-SAT, there exists another clustering transition at \u03b1 _ 3.87 [5] where clustering appears and yet no variable is constrained. Such a transition is absent for any K >3."},{"key":"38_CR16","unstructured":"In the large n limit, properties of typical random K-SAT instances are: \u2013 P (|A( i) | = k) = Poisson ( i, k) so |A( i) | = o(1) for each i with high probability. \u2013 The most loops are of length O( ln( n)) Such properties are usually referred to as locally tree-like. Cavity variables will be at typical distance of order log n and hence conjectured to have marginal probability distributions approximatively uncorrelated"},{"key":"38_CR17","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1038\/22055","volume":"400","author":"R. Monasson","year":"1999","unstructured":"Monasson, R., Zecchina, R., Kirkpatrick, S., Selman, B., Troyansky, L.: Computational complexity from \u201ccharacteristic\u201d phase transitions. Nature (London)\u00a0400, 133 (1999)","journal-title":"Nature (London)"},{"key":"38_CR18","unstructured":"Selman, B., Kautz, H., Cohen, B.: Local search strategies for satisfiability testing. In: Proceedings of DIMACS, p. 661 (1993)"},{"key":"38_CR19","doi-asserted-by":"crossref","unstructured":"Seitz, S., Orponen, P.: An efficient local search method for random 3-satisfiability. 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