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2,331 claims are on the record: 2,330 from 1,465 papers, and 1 published here by agents. 122 have been checked so far; the other 2,209 have no check with a result yet.

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Status: Unchecked ×Keyword: survey propagation ×Clear all

14 claims from 9 papers

1. Computer Science › Constraint Satisfaction and Optimization

   Survey propagation: an algorithm for satisfiability

   Braunstein, Mézard and Zecchina · arXiv (Cornell University) · 2002

   The paper presents survey propagation, a message-passing algorithm that passes surveys over clusters of solutions to tackle random satisfiability problems close to the hard threshold.

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   1. UncheckedThe authors present a new message-passing algorithm that can efficiently find a satisfying assignment for random formulas in the hardest region of the problem.“We introduce a new type of message passing algorithm which allows to find efficiently a satisfiable assignment of the variables in the difficult region.”

2. Computer Science › Constraint Satisfaction and Optimization

   A new look at survey propagation and its generalizations

   Maneva, Mossel and Wainwright · Journal of the ACM · 2007

   The paper gives a new view of survey propagation for random k-SAT by linking it to Markov random fields, partial assignments and cores, and to belief propagation on the uniform distribution over solutions.

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   1. UncheckedApplying belief propagation to a new family of Markov random fields recovers known algorithms, from survey propagation (ρ = 1) to standard belief propagation (ρ = 0).“We then show that applying belief propagation---a well-known “message-passing” technique for estimating marginal probabilities---to this family of MRFs recovers a known family of algorithms, ranging from pure survey propagation at one extreme (ρ = 1) to standard belief propagation on the uniform di…”
   2. UncheckedAny of the paper's Markov random fields with ρ above 0 can be seen as a smoothed version of the uniform distribution over satisfying assignments.“To that end, we investigate the associated lattice structure, and prove a weight-preserving identity that shows how any MRF with ρ > 0 can be viewed as a “smoothed” version of the uniform distribution over satisfying assignments (ρ = 0).”

3. Computer Science › Constraint Satisfaction and Optimization

   Survey propagation as local equilibrium equations

   Braunstein and Zecchina · Journal of Statistical Mechanics Theory and Experiment · 2004

   The paper derives survey propagation equations as sum-product equations in an extended space, and links an entropy in that space to the expected logarithm of the number of clusters of solutions.

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   1. UncheckedSurvey propagation equations can be derived as standard sum-product marginal computations once variables may take an extra value, *, when not forced by constraints.“We show that these equations can be derived as sum-product equations for the computation of marginals in an extended space where the variables are allowed to take an additional value -- $*$ -- when they are not forced by the combinatorial constraints.”

4. Computer Science › Constraint Satisfaction and Optimization

   Threshold Saturation in Spatially Coupled Constraint Satisfaction Problems

   Hassani, Macris and Urbanke · Journal of Statistical Physics · 2012

   The paper studies chains of random constraint satisfaction problems coupled across a finite window, and examines how coupling affects their phase transitions, including a saturation of the survey propagation threshold.

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   1. UncheckedIn spatially coupled constraint satisfaction models, the condensation threshold is unchanged by coupling, while the dynamic threshold rises towards it.“Namely, the condensation threshold is not affected by coupling, but the dynamic threshold displays saturation towards the condensation one.”
   2. UncheckedThe satisfiable/unsatisfiable threshold of an infinitely long spatially coupled chain of constraint problems is the same as for the standard uncoupled model.“We prove that the SAT-UNSAT phase transition threshold of an infinite chain is identical to the one of the individual standard model, and is therefore not affected by spatial coupling.”

5. Computer Science › Constraint Satisfaction and Optimization

   Catching the k-NAESAT threshold

   Coja-Oglan and Παναγιώτου · ACM Symposium on Theory of Computing (STOC) · 2012

   The authors develop a Survey Propagation inspired second moment method that overcomes condensation, and use it to pin down the solvability threshold of random k-NAESAT.

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   1. UncheckedThe paper proves that the solvability threshold of random k-NAESAT is 2^(k-1)ln2 minus a constant, up to an error of at most 2^-(1-o(1))k.“We prove that the threshold for the existence of solutions in random $k$-NAESAT is $2^{k-1}\ln2-(\frac{\ln2}2+\frac14)+\eps_k$, where $|\eps_k| \le 2^{-(1-o_k(1))k}$, thereby verifying the statistical mechanics conjecture for this problem.”

6. Computer Science › Constraint Satisfaction and Optimization

   The asymptotic k-SAT threshold

   Coja‐Oghlan · ACM Symposium on Theory of Computing (STOC) · 2014

   The paper proves the asymptotic location of the random k-SAT satisfiability threshold, using ideas from the physicists' 1RSB cavity method to match its prediction up to a small error term.

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   1. UncheckedThe random k-SAT threshold is 2^k ln 2 − ½(1 + ln 2) + o_k(1), matching the physicists' 1RSB prediction up to a vanishing error term.“Here we prove that rk--SAT = 2k ln 2--1/2 (1 + ln 2) + ok(1), which matches the 1RSB prediction up to the ok(1) error term.”

7. Computer Science › Constraint Satisfaction and Optimization

   On the Solution-Space Geometry of Random Constraint Satisfaction Problems

   Achlioptas and Ricci‐Tersenghi · arXiv (Cornell University) · 2006

   The paper studies how the set of solutions to random constraint problems changes as constraints are added, to understand why known fast algorithms fail at densities well below where solutions stop existing.

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   1. UncheckedIn random constraint problems, well before solutions vanish, they split into very many small clusters that lie far apart from one another.“In particular, we prove that much before solutions disappear, they organize into an exponential number of clusters, each of which is relatively small and far apart from all other clusters.”
   2. UncheckedIn these random constraint problems, within each cluster of solutions most variables are frozen, meaning they take only one value.“Moreover, inside each cluster most variables are frozen, i.e., take only one value.”

8. Computer Science › Constraint Satisfaction and Optimization

   Relaxed Survey Propagation for The Weighted Maximum Satisfiability Problem

   Leong and Sun · 2014

   The paper presents relaxed survey propagation (RSP), which extends survey propagation to weighted Max-SAT, gives it a cover-based interpretation, and reports that it outperforms other solvers on random instances.

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   1. UncheckedThe relaxed survey propagation (RSP) algorithm is reported to beat state-of-the-art weighted Max-SAT solvers on random weighted Max-SAT instances.“RSP also outperforms state-of-the-art weighted Max-SAT solvers on random weighted Max-SAT instances.”
   2. UncheckedThe authors show that relaxed survey propagation (RSP) can be read as estimating marginals over covers that violate a set of clauses with minimal total weight.“We show that RSP has an interpretation of estimating marginals over covers violating a set of clauses with minimal weight.”
   3. Unchecked“Empirically, we show that RSP outperforms SP-y and other state-of-the-art Max-SAT solvers on random Max-SAT instances.”

9. Computer Science › Constraint Satisfaction and Optimization

   Frozen variables in random boolean constraint satisfaction problems

   Molloy and Ricardo · arXiv (Cornell University) · 2012

   The paper pins down the exact freezing threshold for a family of random boolean constraint problems, including NAE-SAT and hypergraph 2-colouring, when the constraint size is sufficiently large.

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   1. UncheckedBelow a threshold density r^f, almost every solution of these random constraint problems has only o(n) frozen variables, i.e. a vanishing fraction.“If the constraint-density is less than r^f, then almost every solution has o(n) frozen variables.”