Branching structures emerging from a continuous optimal transport model

Facca, Enrico; Cardin, Franco; Putti, Mario

doi:10.1016/j.jcp.2021.110700

Cited by 21 publications

(35 citation statements)

References 26 publications

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“…In this work, we developed a robust and fast model able to perform this task finding stationary solutions of a dynamical system controlling fluxes and conductivities of edges. Our dynamics extends previous works focusing solely on the uni-commodity [15,27,28,30,41], and on the multicommodity setup [25,26,34].…”

Section: Discussionsupporting

confidence: 63%

“…A promising approach is that of optimal transport theory. Recent studies [25,26] have shown that this theoretical formalism can be adapted to address multicommodity scenarios, generalizing well-established results for unicommodity models [27][28][29][30][31][32][33]. The works of Lonardi et al [25] and Bonifaci et al [26] focus on a theoretical characterization of the problem, drawing a formal connection between optimal transport and an equivalent dynamical system that is formulated in terms of physical quantities like conductivities and fluxes.…”

Section: Introductionmentioning

confidence: 81%

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Multicommodity routing optimization for engineering networks

Lonardi,

Putti,

De Bacco

2021

Preprint

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Optimizing passengers routes is crucial to design efficient transportation networks. Recent results show that optimal transport provides an efficient alternative to standard optimization methods. However, it is not yet clear if this formalism has empirical validity on engineering networks. We address this issue by considering different response functions-quantities determining the interaction between passengers-in the dynamics implementing the optimal transport formulation. Particularly, we compare a theoretically-grounded response function with one that is intuitive for settings involving transportation of passengers, albeit lacking theoretical justifications. We investigate these two modeling choices on the Paris metro and analyze how they reflect on passengers' fluxes. We measure the extent of traffic bottlenecks and infrastructure resilience to node removal, showing that the two settings are equivalent in the congested transport regime, but different in the branched one. In the latter, the two formulations differ on how fluxes are distributed, with one function favoring routes consolidation, thus potentially being prone to generate traffic overload. Additionally, we compare our method to Dijkstra's algorithm to show its capacity to efficiently recover shortest-path-like graphs. Finally, we observe that optimal transport networks lie in the Pareto front drawn by the energy dissipated by passengers, and the cost to build the infrastructure.

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Section: Discussionsupporting

confidence: 63%

Section: Introductionmentioning

confidence: 81%

Multicommodity routing optimization for engineering networks

Lonardi,

Putti,

De Bacco

2021

Preprint

Self Cite

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“…In this section, we describe the main ideas and establish notation. We start by introducing the dynamical system of equations corresponding to the DMK routing optimization problem as proposed by Facca et al [25][26][27] In these works, the authors first generalize the discrete dynamics of the slime mold Physarum Polycephalum (PP) to a continuous domain; then they conjecture that, like its discrete counterpart, its solution tends to an equilibrium point which is the solution of the Monge-Kantorovich optimal mass transport 42 as time goes to infinity.…”

Section: The Routing Optimization Problemmentioning

confidence: 99%

“…While the theory starts to consolidate, efficient numerical methods are still in a pre-development stage, in particular in the case of branched transport, where only a few results are present 23,24 , reflecting the obstacle that all these problems have an NP-hard genesis. Recent promising results 25,26 map a computationally hard optimization problem into finding the long-time behavior of a system of dynamic partial differential equations, the so-called Dynamic Monge-Kantorovich (DMK) approach, which is instead numerically accessible, computationally efficient, and leads to network shapes that resemble optimal structures 27 . Working in discretized continuous space, and in many network-based discretizations such as lattice-like networks as well, requires the use of threshold values for the identification of active network edges.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we propose a new approach for the extraction of network topologies and build a protocol to address this problem. This can take in input the numerical solution of a routing optimization problem in continuous space as described in [25][26][27] and then processes it to finally output the corresponding network topology in terms of a weighted adjacency matrix. However, it can also be applied to more general inputs, such as images, which may not necessarily come from the solution of an explicit routing transportation problem.…”

Section: Introductionmentioning

confidence: 99%

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Network extraction by routing optimization

Baptista,

Leite,

Facca

et al. 2020

Preprint

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Routing optimization is a relevant problem in many contexts. Solving directly this type of optimization problem is often computationally unfeasible. Recent studies suggest that one can instead turn this problem into one of solving a dynamical system of equations, which can instead be solved efficiently using numerical methods. This results in enabling the acquisition of optimal network topologies from a variety of routing problems. However, the actual extraction of the solution in terms of a final network topology relies on numerical details which can prevent an accurate investigation of their topological properties. In fact, in this context, theoretical results are fully accessible only to an expert audience and ready-to-use implementations for non-experts are rarely available or insufficiently documented. In particular, in this framework, final graph acquisition is a challenging problem in-and-of-itself. Here we introduce a method to extract networks topologies from dynamical equations related to routing optimization under various parameters' settings. Our method is made of three steps: first, it extracts an optimal trajectory by solving a dynamical system, then it pre-extracts a network and finally, it filters out potential redundancies. Remarkably, we propose a principled model to address the filtering in the last step, and give a quantitative interpretation in terms of a transport-related cost function. This principled filtering can be applied to more general problems such as network extraction from images, thus going beyond the scenarios envisioned in the first step. Overall, this novel algorithm allows practitioners to easily extract optimal network topologies by combining basic tools from numerical methods, optimization and network theory. Thus, we provide an alternative to manual graph extraction which allows a grounded extraction from a large variety of optimal topologies. The analysis of these may open up the possibility to gain new insights into the structure and function of optimal networks. Our algorithm is open source and available at https://github.com/Danielaleite/NextRout.

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Convergence Properties of Optimal Transport-Based Temporal Networks

Baptista

Bacco

2022

Complex Networks &Amp; Their Applications X

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Branching structures emerging from a continuous optimal transport model

Cited by 21 publications

References 26 publications

Multicommodity routing optimization for engineering networks

Multicommodity routing optimization for engineering networks

Network extraction by routing optimization

Convergence Properties of Optimal Transport-Based Temporal Networks

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