Related papers: Hiding Quiet Solutions in Random Constraint Satisf…
We study the planted ensemble of locked constraint satisfaction problems. We describe the connection between the random and planted ensembles. The use of the cavity method is combined with arguments from reconstruction on trees and first…
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…
We study the phase diagram and the algorithmic hardness of the random `locked' constraint satisfaction problems, and compare them to the commonly studied 'non-locked' problems like satisfiability of boolean formulas or graph coloring. The…
The set of solutions of random constraint satisfaction problems (zero energy groundstates of mean-field diluted spin glasses) undergoes several structural phase transitions as the amount of constraints is increased. This set first breaks…
We discuss an analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring, in terms of an effective energy landscape. Several intriguing geometrical properties of the solution space become in this light…
Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…
The typical complexity of Constraint Satisfaction Problems (CSPs) can be investigated by means of random ensembles of instances. The latter exhibit many threshold phenomena besides their satisfiability phase transition, in particular a…
We present a theoretical framework for characterizing the geometrical properties of the space of solutions in constraint satisfaction problems, together with practical algorithms for studying this structure on particular instances. We apply…
We introduce and study the random "locked" constraint satisfaction problems. When increasing the density of constraints, they display a broad "clustered" phase in which the space of solutions is divided into many isolated points. While the…
An instance of a random constraint satisfaction problem defines a random subset S (the set of solutions) of a large product space (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and…
We present an exactly solvable random-subcube model inspired by the structure of hard constraint satisfaction and optimization problems. Our model reproduces the structure of the solution space of the random k-satisfiability and k-coloring…
Planting a solution into the random RB model, which is a prototype of random constraint satisfaction problem (CSP) with growing domains, can generate very hard satisfiable CSP benchmarks. We study the solution space structure of the planted…
Random constraint satisfaction problems play an important role in computer science and combinatorics. For example, they provide challenging benchmark instances for algorithms and they have been harnessed in probabilistic constructions of…
Random constraint satisfaction problems undergo several phase transitions as the ratio between the number of constraints and the number of variables is varied. When this ratio exceeds the satisfiability threshold no more solutions exist;…
We describe an effective landscape introduced in [1] for the analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring. This geometric construction reexpresses these problems in the more familiar terms…
This paper studies a class of probabilistic models on graphs, where edge variables depend on incident node variables through a fixed probability kernel. The class includes planted con- straint satisfaction problems (CSPs), as well as more…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
We study the detection problem of finding planted solutions in random instances of flat satisfiability problems, a generalization of boolean satisfiability formulas. We describe the properties of random instances of flat satisfiability, as…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…