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. We also …

We study in this paper the structure of solutions in the random hypergraph coloring problem
and the phase transitions they undergo when the density of constraints is varied …

We study constraint satisfaction problems on the so-called planted random ensemble. We
show that for a certain class of problems, eg, graph coloring, many of the properties of the …

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 …

Random constraint satisfaction problems exhibit several phase transitions when their
density of constraints is varied. One of these threshold phenomena, known as the clustering …

Optimization is fundamental in many areas of science, from computer science and
information theory to engineering and statistical physics, as well as to biology or social …

Circular coloring is a constraint satisfaction problem where colors are assigned to nodes in a
graph in such a way that every pair of connected nodes has two consecutive colors (the first …

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 …

An instance of a random constraint satisfaction problem defines a random subset 𝒮 (the set
of solutions) of a large product space XN (the set of assignments). We consider two …

For many random constraint satisfaction problems, by now there exist asymptotically tight
estimates of the largest constraint density for which solutions exist. At the same time, for …