# The Competition for Shortest Paths on Sparse Graphs

@article{Yeung2012TheCF, title={The Competition for Shortest Paths on Sparse Graphs}, author={Chi Ho Yeung and David Saad}, journal={Physical review letters}, year={2012}, volume={108 20}, pages={ 208701 } }

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…

## 24 Citations

Shortest node-disjoint paths on random graphs

- Computer ScienceArXiv
- 2014

A method based on message-passing techniques to process global information and distribute paths optimally to find the shortest paths between given source/destination pairs while avoiding path overlaps at nodes is proposed.

Global benefit of randomness in individual routing on transportation networks.

- Computer SciencePhysical review. E
- 2019

It is found that adaptive routing strategies outperform controlled strategies in the free-flow state but not in the congested state, implying that controlled strategies may increase coordination among vehicles and are beneficial for suppressing traffic congestion.

Efficient algorithm for routing optimization via statistical mechanics

- Computer Science2013 IEEE International Conference on Communications Workshops (ICC)
- 2013

A distributive message-passing algorithm capable of optimizing the path configuration in real instances is devised, based on the analytical derivation, and is greatly simplified by expanding the cost function around the optimized flow.

M ay 2 01 4 Shortest node-disjoint paths on random graphs

- Computer Science
- 2014

A method based on message-passing technology to process global information and distribute paths optimally to find the shortest paths between given source/destinatio n pairs while avoiding path overlaps at nodes is proposed.

Scalable Node-Disjoint and Edge-Disjoint Multi-wavelength Routing

- Computer SciencePhysical review. E
- 2022

The scalable principled method developed is exact on trees but provides good approximate solutions on locally treelike graphs and provides the tool for settling an open and much-debated question on the merit of wavelength-switching nodes and the added capabilities they provide.

Self-organization scheme for balanced routing in large-scale multi-hop networks

- Computer ScienceArXiv
- 2018

This work applies belief propagation (its min-sum version) to solve the network optimization problem and obtains a distributed algorithm whereby the nodes collectively discover globally optimal routes by performing low-complexity computations and exchanging messages with their neighbours.

The Edge-Disjoint Path Problem on Random Graphs by Message-Passing

- Computer SciencePloS one
- 2015

A message-passing algorithm to solve a series of edge-disjoint path problems on graphs based on the zero-temperature cavity equations is presented, able to always outperform the other algorithms with a peak of 27% performance improvement in terms of accommodated paths.

Routing optimization in networks based on traffic gravitational field model

- Computer Science
- 2017

This study introduces the concept of path confidence degree to evaluate the unblocked reliability of paths that it takes the traffic state of all nodes on the path into account from the overall and proposes an improved gravitational field routing protocol considering all the nodes’ gravities on thePath confidence degree.

From the physics of interacting polymers to optimizing routes on the London Underground

- Computer ScienceProceedings of the National Academy of Sciences
- 2013

This work uses the physics of interacting polymers and disordered systems to analyze macroscopic properties of generic path optimization problems and derives a simple, principled, generic, and distributed routing algorithm capable of considering all individual path choices simultaneously.

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