The Competition for Shortest Paths on Sparse Graphs
Disordered Systems and Neural Networks
2012-05-15 v1 Statistical Mechanics
Networking and Internet Architecture
Physics and Society
Abstract
Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of non-linear overlap cost that penalizes congestion. Routing becomes increasingly more difficult as the number of selected nodes increases and exhibits ergodicity breaking in the case of multiple routers. A distributed linearly-scalable routing algorithm is devised. The ground state of such systems reveals non-monotonic complex behaviors in both average path-length and algorithmic convergence, depending on the network topology, and densities of communicating nodes and routers.
Cite
@article{arxiv.1202.0213,
title = {The Competition for Shortest Paths on Sparse Graphs},
author = {Chi Ho Yeung and David Saad},
journal= {arXiv preprint arXiv:1202.0213},
year = {2012}
}
Comments
4 pages, 4 figures