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1,168 claims from 737 papers are on the record. 44 have been checked so far; the other 1,124 have no check with a result yet.

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Status: Unchecked ×Topic: Constraint Satisfaction and Optimization ×Clear all

87 claims from 57 papers, showing 21–40 of 57

1. Computer Science › Constraint Satisfaction and Optimization

   Statistical mechanics of the random K -satisfiability model

   Monasson and Zecchina · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1997

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   1. Unchecked“The annealed approximation is proven to be exact for large K.”

2. Computer Science › Constraint Satisfaction and Optimization

   Threshold Saturation in Spatially Coupled Constraint Satisfaction Problems

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

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   1. Unchecked“Namely, the condensation threshold is not affected by coupling, but the dynamic threshold displays saturation towards the condensation one.”
   2. Unchecked“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.”

3. Computer Science › Constraint Satisfaction and Optimization

   Reconstruction and Clustering in Random Constraint Satisfaction Problems

   A, Restrepo and Tetali · SIAM Journal on Discrete Mathematics · 2011

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   1. Unchecked“The bounds become asymptoticlally tight as the number of degrees of freedom in each clause diverges.”

4. Computer Science › Constraint Satisfaction and Optimization

   On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms

   Ricci-Tersenghi and Semerjian · Journal of Statistical Mechanics Theory and Experiment · 2009

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   1. Unchecked“We introduce a version of the cavity method for diluted mean-field spin models that allows the computation of thermodynamic quantities similar to the Franz-Parisi quenched potential in sparse random graph models.”

5. Computer Science › Constraint Satisfaction and Optimization

   A Better Algorithm for Random k -SAT

   Coja‐Oghlan · SIAM Journal on Computing · 2010

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   1. Unchecked“We present a polynomial time algorithm that finds a satisfying assignment of F with high probability for constraint densities m/n<(1-eps_k)2^k\ln(k)/k, where eps_k->0.”

6. Computer Science › Constraint Satisfaction and Optimization

   Constraint satisfaction problems with isolated solutions are hard

   Zdeborová and Mézard · Journal of Statistical Mechanics Theory and Experiment · 2008

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   1. Unchecked“On the other hand we show empirically that the clustered phase of these problems is extremely hard from the algorithmic point of view: the best known algorithms all fail to find solutions.”

7. Computer Science › Constraint Satisfaction and Optimization

   Locked Constraint Satisfaction Problems

   Zdeborová and Mézard · Physical Review Letters · 2008

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   1. Unchecked“While the phase diagram can be found easily, these problems, in their clustered phase, are extremely hard from the algorithmic point of view: the best known algorithms all fail to find solutions.”

8. Computer Science › Constraint Satisfaction and Optimization

   Catching the k-NAESAT threshold

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

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   1. Unchecked“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.”

9. Computer Science › Constraint Satisfaction and Optimization

   The freezing threshold for k-colourings of a random graph

   Molloy · ACM Symposium on Theory of Computing (STOC) · 2012

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   1. Unchecked“We prove that for random graphs with density above rkf, almost every colouring is such that a linear number of variables are frozen, meaning that their colours cannot be changed by a sequence of alterations whereby we change the colours of o(n) vertices at a…
   2. Unchecked“When the density is below rkf, then almost every colouring has at most o(n) frozen variables.”

10. Computer Science › Constraint Satisfaction and Optimization

    The asymptotic k-SAT threshold

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

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    1. Unchecked“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.”

11. Computer Science › Constraint Satisfaction and Optimization

    Proof of the satisfiability conjecture for large k

    Ding, Sly and Sun · arXiv (Cornell University) · 2014

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    1. Unchecked“We establish the satisfiability threshold for random $k$-SAT for all $k\ge k_0$, with $k_0$ an absolute constant.”
    2. Unchecked“We show that the threshold $α_*(k)$ is given explicitly by the one-step replica symmetry breaking prediction from statistical physics.”

12. Computer Science › Constraint Satisfaction and Optimization

    Proof of the satisfiability conjecture for large $k$

    Ding, Sly and Sun · Annals of Mathematics · 2022

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    1. Unchecked“We establish the satisfiability threshold for random $k$-SAT for all $k\ge k_0$, with $k_0$ an absolute constant.”
    2. Unchecked“We show that the threshold $\alpha_{\rm sat}(k)$ is given explicitly by the one-step replica symmetry breaking prediction from statistical physics.”

13. Computer Science › Constraint Satisfaction and Optimization

    An Analysis of Phase Transition in NK Landscapes

    Gao and Culberson · Journal of Artificial Intelligence Research · 2002

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    1. Unchecked“For the fixed ratio model, we establish several upper bounds for the solubility threshold, and prove that random instances with parameters above these upper bounds can be solved polynomially.”
    2. Unchecked“For the uniform probability model, we prove that the phase transition is easy in the sense that there is a polynomial algorithm that can solve a random instance of the problem with the probability asymptotic to 1 as the problem size tends to infinity.”

14. Computer Science › Constraint Satisfaction and Optimization

    Biased landscapes for random constraint satisfaction problems

    Budzynski, Ricci‐Tersenghi and Semerjian · Journal of Statistical Mechanics Theory and Experiment · 2019

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    1. Unchecked“We show that for small k the clustering transition can be delayed in this way to higher density of constraints, and that this strategy has a positive impact on the performances of Simulated Annealing algorithms.”

15. Computer Science › Constraint Satisfaction and Optimization

    Analytical and belief-propagation studies of random constraint satisfaction problems with growing domains

    Zhao, Zhang, Zheng and Xu · Physical Review E · 2012

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    1. Unchecked“Using rigorous methods, we show that solutions are grouped into disconnected clusters before the theoretical satisfiability phase transition point.”
    2. Unchecked“From an algorithmic point of view, we find that reinforced BP, which performs much better than all existing algorithms, allows us to find solutions efficiently for instances in the regime that is very close to the satisfiability transition.”

16. Computer Science › Constraint Satisfaction and Optimization

    Phase transitions in the q -coloring of random hypergraphs

    Gabrié, Dani, Semerjian and Zdeborová · Journal of Physics A Mathematical and Theoretical · 2017

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    1. Unchecked“Among other cases we revisit the hypergraph bicoloring problem ($q=2$) where we find that for $K=3$ and $K=4$ the colorability threshold is not given by the one-step-replica-symmetry-breaking analysis as the latter is unstable towards more levels of replica…
    2. Unchecked“We also unveil and discuss the coexistence of two different 1RSB solutions in the case of $q=2$, $K \ge 4$.”

17. Computer Science › Constraint Satisfaction and Optimization

    The number of satisfying assignments of random 2‐SAT formulas

    Achlioptas, Coja‐Oghlan, Hahn‐Klimroth et al. · Random Structures and Algorithms · 2021

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    1. Unchecked“The proof is based on showing that the Belief Propagation algorithm renders the correct marginal probability that a variable is set to `true' under a uniformly random satisfying assignment.”
    2. Unchecked“We show that throughout the satisfiable phase the normalised number of satisfying assignments of a random $2$-SAT formula converges in probability to an expression predicted by the cavity method from statistical physics.”

18. Computer Science › Constraint Satisfaction and Optimization

    On the empirical time complexity of random 3-SAT at the phase transition

    Mu and Hoos · International Conference on Artificial Intelligence · 2015

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    1. Unchecked“An analogous analysis of three complete, DPLL-based solvers - kcnfs, march_hi and march_br - clearly indicates exponential scaling of median running time.”
    2. Unchecked“Moreover, exponential scaling is witnessed for these DPLL-based solvers when solving only satisfiable and only unsatisfiable instances, and the respective scaling models for each solver differ mostly by a constant factor.”

19. Computer Science › Constraint Satisfaction and Optimization

    Phase transitions of the typical algorithmic complexity of the random satisfiability problem studied with linear programming

    Schawe, Bleim and Hartmann · PLoS ONE · 2019

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    1. Unchecked“For the present random $K$-SAT problem we have investigated numerous structural properties also exhibiting clear transitions, but they appear not be correlated to the here observed easy-hard transitions.”

20. Computer Science › Constraint Satisfaction and Optimization

    The Freezing Threshold for k -Colourings of a Random Graph

    Molloy · Journal of the ACM · 2018

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    1. Unchecked“We prove that for random graphs with density above r f k , almost every colouring is such that a linear number of vertices are frozen, meaning that their colour cannot be changed by a sequence of alterations whereby we change the colours of o ( n ) vertices…
    2. Unchecked“When the density is below r f k , then almost every colouring is such that every vertex can be changed by a sequence of alterations where we change O (log n ) vertices at a time.”