The Competition for Shortest Paths on Sparse Graphs

TL;DR

This paper analyzes optimal path routing on sparse graphs with congestion costs, revealing complex behaviors and proposing a scalable distributed routing algorithm.

Contribution

It introduces a new analytical framework for congestion-aware routing and a scalable distributed algorithm for sparse networks.

Findings

Routing complexity increases with node number

Multiple routers cause ergodicity breaking

Non-monotonic behaviors in path-length and convergence

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.