Abstract
It has been shown experimentally that a decimation algorithm based on survey propagation (SP)equations allows one to solve efficiently some combinatorial problems over random graphs. Weshow that these equations can be derived as sum–product equations for the computation ofmarginals in an extended space where the variables are allowed to take an additionalvalue—*—when they are not forced by the combinatorial constraints. An appropriate ‘local equilibriumcondition’ cost/energy function is introduced and its entropy is shown to coincide with theexpected logarithm of the number of clusters of solutions as computed by SP. These resultsmay help to clarify the geometrical notion of clusters assumed by SP for randomK-SAT or random graph colouring (where it is conjectured to be exact) and help to explainwhich kind of clustering operation or approximation is enforced in general/small sizedmodels in which it is known to be inexact.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Statistical Mechanics: Theory and Experiment
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
