Publication

The Costly Path from Percolation to Full Connectivity

Patrick Thiran
2004
Conference Papers

Abstract

Requiring all nodes of a wireless multihop network to be connected is expensive and results in a poor scalability of properties such as transport capacity. We show however that it is no longer the case if we only slightly loosen the connectivity requirement, by just imposing that most nodes be connected to each other (so that the network percolates). This feature is found in models neglecting interferences, taking interferences as noise or taking a more information theoretic approach.

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Patrick Thiran
2004
Conference Papers

Abstract

Official source

Related concepts (32)

Percolation theory

In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters. The applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles Network theory and Percolation (cognitive psychology).

Percolation

In physics, chemistry, and materials science, percolation () refers to the movement and filtering of fluids through porous materials. It is described by Darcy's law. Broader applications have since been developed that cover connectivity of many systems modeled as lattices or graphs, analogous to connectivity of lattice components in the filtration problem that modulates capacity for percolation.

Percolation threshold

The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size. In engineering and coffee making, percolation represents the flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified lattice models of random systems or networks (graphs), and the nature of the connectivity in them.

Related publications (2)

The Costly Path from Percolation to Full Connectivity

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