# 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 Science, MathematicsArXiv
- 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.

- Physics, MathematicsPhysical 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

- 2014

A localized method to distribute paths on random graphs is de vised, aimed at finding the shortest paths between given source/destinatio n pairs while avoiding path overlaps at nodes. We propose a…

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

- Computer Science, PhysicsArXiv
- 2021

The scalable principled method developed is exact on trees but provides good approximate solutions on locally tree-like 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 Science, PhysicsArXiv
- 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 Science, MedicinePloS 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.

Maximum transport capacity of a network

- Computer Science
- 2015

The results demonstrate that the maximum transport capacity of a network, which is the essential characteristic of the network, is mainly determined by the topological structure of thenetwork and is independent of the routing strategies.

Routing optimization in networks based on traffic gravitational field model

- Physics
- 2017

For research on the gravitational field routing mechanism on complex networks, we further analyze the gravitational effect of paths. In this study, we introduce the concept of path confidence degree…

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

- Computer Science, PhysicsProceedings 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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