Matching Algorithms Are Fast in Sparse Random Graphs

Push is Fast on Sparse Random Graphs

We consider the classical push broadcast process on a large class of sparse random multigraphs that includes random power law graphs and multigraphs. Our analysis shows that for every ε > 0, whp O(log n) rounds are sufficient to inform all but an ε-fraction of the vertices. It is not hard to see that, e.g. for random power law graphs, the push process needs whp n rounds to inform all vertices. ...

Fast Generation of Sparse Random Kernel Graphs

The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algor...

Sparse pseudo-random graphs are Hamiltonian

In this article we study Hamilton cycles in sparse pseudorandom graphs. We prove that if the second largest absolute value of an eigenvalue of a d-regular graph G on n vertices satisfies

Statistical Mechanics and Algorithms on Sparse and Random Graphs

Models of Sparse Random Graphs and Network Algorithms

There is no doubt now that the current trend that every electronic device should be connected in one way or another (usually many) implies a greater need for efficient networks. These networks should be connected, exhibit small-world behavior and their topology should be robust to local modifications like device movement; all this should be achieved using minimal and distributed processes. The ...