The combination of the compactness of networks, featuring small diameters, and their
complex architectures results in a variety of critical effects dramatically different from those in …

We study the problem of satisfiability of randomly chosen clauses, each with K Boolean
variables. Using the cavity method at zero temperature, we find the phase diagram for the K …

We consider the problem of coloring the vertices of a large sparse random graph with a
given number of colors so that no adjacent vertices have the same color. Using the cavity …

This article provides a new conceptual perspective on survey propagation, which is an
iterative algorithm recently introduced by the statistical physics community that is very …

A variational approach to finite connectivity spin-glass-like models is developed and applied
to describe the structure of optimal solutions in random satisfiability problems. Our …

Computer science and physics have been closely linked since the birth of modern
computing. In recent years, an interdisciplinary area has blossomed at the junction of these …

We investigate the phase transition in vertex coloring on random graphs, using the extremal
optimization heuristic. Three-coloring is among the hardest combinatorial optimization …

An analysis of the average properties of a local search procedure (RandomWalkSAT) for the
satisfaction of random Boolean constraints is presented. Depending on the ratio α of …

This paper presents an experimental investigation of the following questions: how does the
average-case complexity of random 3-SAT, understood as a function of the order (number of …

In this paper, we are interested in a particular combinatorial optimisation problem (COP),
namely the graph colouring problem (GCP). To solve the GCP, we present a parallel …