Competition for Shortest Paths on Sparse Graphs
Abstract
Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of a nonlinear overlap cost that penalizes congestion. Routing becomes more difficult as the number of selected nodes increases and exhibits ergodicity breaking in the case of multiple routers. The ground state of such systems reveals nonmonotonic complex behaviors in average path length and algorithmic convergence, depending on the network topology, and densities of communicating nodes and routers. A distributed linearly scalable routing algorithm is also devised.
 Publication:

Physical Review Letters
 Pub Date:
 May 2012
 DOI:
 10.1103/PhysRevLett.108.208701
 arXiv:
 arXiv:1202.0213
 Bibcode:
 2012PhRvL.108t8701Y
 Keywords:

 89.75.Hc;
 02.50.r;
 05.20.y;
 89.20.a;
 Networks and genealogical trees;
 Probability theory stochastic processes and statistics;
 Classical statistical mechanics;
 Interdisciplinary applications of physics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics;
 Computer Science  Networking and Internet Architecture;
 Physics  Physics and Society
 EPrint:
 4 pages, 4 figures