Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-10-06
Physical Review E 71, 046133, 2005
Physics
Condensed Matter
Disordered Systems and Neural Networks
11 Pages, 5 Postscript figures; added references, expanded on protocol discussion
Scientific paper
10.1103/PhysRevE.71.046133
The maximum entropy principle from statistical mechanics states that a closed system attains an equilibrium distribution that maximizes its entropy. We first show that for graphs with fixed number of edges one can define a stochastic edge dynamic that can serve as an effective thermalization scheme, and hence, the underlying graphs are expected to attain their maximum-entropy states, which turn out to be Erdos-Renyi (ER) random graphs. We next show that (i) a rate-equation based analysis of node degree distribution does indeed confirm the maximum-entropy principle, and (ii) the edge dynamic can be effectively implemented using short random walks on the underlying graphs, leading to a local algorithm for the generation of ER random graphs. The resulting statistical mechanical system can be adapted to provide a distributed and local (i.e., without any centralized monitoring) mechanism for load balancing, which can have a significant impact in increasing the efficiency and utilization of both the Internet (e.g., efficient web mirroring), and large-scale computing infrastructure (e.g., cluster and grid computing).
Boykin Patrick Oscar
Bridgewater Jesse S. A.
Roychowdhury Vwani P.
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