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

@article{Altarelli2015TheEP, title={The Edge-Disjoint Path Problem on Random Graphs by Message-Passing}, author={Fabrizio Altarelli and Alfredo Braunstein and Luca Dall’Asta and Caterina De Bacco and Silvio Franz}, journal={PLoS ONE}, year={2015}, volume={10} }

We present a message-passing algorithm to solve a series of edge-disjoint path problems on graphs based on the zero-temperature cavity equations. Edge-disjoint paths problems are important in the general context of routing, that can be defined by incorporating under a unique framework both traffic optimization and total path length minimization. The computation of the cavity equations can be performed efficiently by exploiting a mapping of a generalized edge-disjoint path problem on a star…

## 12 Citations

A Message Passing Algorithm for the Problem of Path Packing in Graphs

- Computer Science, MathematicsArXiv
- 2016

Comparisons show that the proposed new algorithm scales better to large instances than IP-based algorithms and often finds better solutions than a simple algorithm that greedily selects the longest path from each root node.

Solving the edge-disjoint paths problem using a two-stage method

- Computer ScienceInt. Trans. Oper. Res.
- 2020

The proposed approach hybridizes an Integer Linear Programming formulation of the problem with an Evolutionary Algorithm and shows that the proposed procedure compares favorably to previous metaheuristics for this problem.

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- 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.

The cavity approach for Steiner trees Packing problems

- Computer Science, MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2018

A heuristic procedure based on the max-sum equations that shows excellent performance in synthetic networks and on large benchmark instances of VLSI for which the optimal solution is known, on which the algorithm found the optimum in two cases and the gap to optimality was never larger than 4 %.

Solving the maximum edge disjoint path problem using a modified Lagrangian particle swarm optimisation hybrid

- Computer ScienceEur. J. Oper. Res.
- 2021

The LaPSO algorithm, which draws on ideas from both mathematical programming and evolutionary algorithms, is able to outperform both MIP and metaheuristic solvers that only use ideas from one of these areas, making it a “quasi-exact” method.

Decentralized network control, optimization and random walks on networks

- 2015

In the last years several problems been studied at the interface between statistical physics and computer science. The reason being that often these problems can be reinterpreted in the language of…

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.

Coordinating dynamical routes with statistical physics on space-time networks.

- Medicine, PhysicsPhysical review. E
- 2019

This paper first applies the cavity approach in statistical physics to derive the theoretical behavior and an optimization algorithm for dynamical route coordination, then maps static spatial networks to space-time networks to derive a computational feasible message-passing algorithm compatible with arbitrary system parameters.

Multicommodity routing optimization for engineering networks

- Physics, Mathematics
- 2021

Optimizing passengers routes is crucial to design efficient transportation networks. Recent results show that optimal transport provides an efficient alternative to standard optimization methods.…

Vehicle routing in urban areas based on the Oil Consumption Weight -Dijkstra algorithm

- Engineering
- 2016

In this study, the authors refine a route-planning algorithm, in order to improve the route planning strategy in urban areas under traffic congestion. Considering the Oil Consumption Weight (OCW) and…

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