# Phase Transitions and Computational Difficulty in Random Constraint Satisfaction Problems

@article{Krzakala2007PhaseTA, title={Phase Transitions and Computational Difficulty in Random Constraint Satisfaction Problems}, author={Florent Krzakala and Lenka Zdeborov{\'a}}, journal={ArXiv}, year={2007}, volume={abs/0711.0110} }

We review the understanding of the random constraint satisfaction problems, focusing on the q-coloring of large random graphs, that has been achieved using the cavity method of the physicists. We also discuss the properties of the phase diagram in temperature, the connections with the glass transition phenomenology in physics, and the related algorithmic issues.

## 17 Citations

On state space structure and average case complexity in random K-SAT problems

- Computer Science
- 2008

This thesis gives an introduction to a currently active area in the cross-section between theoretical computer science and theoretical physics. In the last ten years it has been suggested that crit…

Boolean constraint satisfaction problems for reaction networks

- Mathematics, Biology
- 2013

By varying a chemical potential attached to the activity of reactions, a class of Boolean constraint satisfaction problems representing minimal feasibility constraints for networks of chemical reactions is defined and first-order transitions and strong hysteresis are found, suggesting a non-trivial structure in the space of feasible solutions.

Biased landscapes for random Constraint Satisfaction Problems

- Physics, Computer ScienceJournal of Statistical Mechanics: Theory and Experiment
- 2019

It is shown 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.

Mean-field disordered systems : glasses and optimization problems, classical and quantum

- Mathematics
- 2013

This manuscript present my research activities in the field of statistical mechanics of disordered systems, in particular mean-field models with finite connectivity. These models exhibit several…

Statistical Physics of Hard Optimization Problems

- Mathematics, PhysicsArXiv
- 2008

A new class of problems is introduced which is named "locked" constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfiability.

Statistical Mechanical Formulation and Simulation of Prime Factorization of Integers

- Mathematics, Physics
- 2013

We propose a new formulation of the problem of prime factorization of integers. With replica exchange Monte Carlo simulation, the behavior which is seemed to indicate exponential computational…

Asymmetric Continuous-Time Neural Networks without Local Traps for Solving Constraint Satisfaction Problems

- Physics, MedicinePloS one
- 2013

It is shown that asymmetric continuous-time neural networks can solve constraint satisfaction problems without getting trapped in non-solution attractors and numerical evidence is presented that limit cycles may also be avoided by appropriately choosing the parameters of the model.

Function simulation, graph grammars and colourings

- Computer Science, MathematicsInt. J. Comput. Math.
- 2013

We prove that to any partial function ϕ defined on a finite set, there corresponds an infinite class of graphs that could be generated by a graph grammar such that each graph in the class represents…

Difficulty Rating of Sudoku Puzzles: An Overview and Evaluation

- Computer ScienceArXiv
- 2014

This work discusses the performance of individual metrics on the Sudoku puzzle, but also on their generalizability and applicability to other problems, and describes metrics based on analysis of solutions under relaxed constraints.

Phase transitions in random Potts systems and the community detection problem: spin-glass type and dynamic perspectives

- Physics
- 2012

Phase transitions in spin-glass type systems and, more recently, in related computational problems have gained broad interest in disparate arenas. In the current work, we focus on the “community…

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