Convergence Properties of Optimal Transport-Based Temporal Networks

Baptista, Diego; Bacco, Caterina De

doi:10.1007/978-3-030-93409-5_48

Cited by 6 publications

(22 citation statements)

References 20 publications

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“…Similarly, it would be interesting to explore how this formalism adapts to multilayer networks, where passengers can enter in different stations corresponding to different transportation modes [20]. Another relevant application could be that of integrating our findings with the recent work of Baptista et al [19], where the authors study how topological properties of the transport network change in time, as we approach stationary configurations, and how these reflect on the shape of the conductivities. Altogether, we believe that our findings extend the current knowledge on network routing problems with time-varying input loads.…”

Section: Discussionmentioning

confidence: 85%

“…Thus, the rank condition on C can be reformulated in terms of an equivalent linear dependence condition of the form ν v = λν u between the vectors ν v , v ∈ V , and for λ = 0. Finally, substituting (19) in this linear dependence condition leads to the following main result. Proposition 1.…”

Section: Conditions For the Generation Of Loops In Closed Formmentioning

confidence: 93%

“…Defining the complex vectors ν v = {c nv v } nv with entries the Fourier coefficients in (19), we rewrite…”

Section: Conditions For the Generation Of Loops In Closed Formmentioning

confidence: 99%

“…Optimized transport of resources is a pivotal contributing factor in determining the structural evolution of real-world networks. Archetypes for self-organizing systems that ramify into networks in order to optimize energy expenditure rates are xylem conduits in leaves [1][2][3][4], river basins [5][6][7][8][9], and slime molds [10][11][12][13][14][15][16][17][18][19]. These formations are not only restricted to the natural realm but can also be generated by anthropogenic processes.…”

Section: Introductionmentioning

confidence: 99%

“…Typically, optimal transport of mass in networks is set as a minimization problem where resources moving through the edges have to satisfy a set of constraints, e.g., conservation of mass, while minimizing a suitable transportation cost [1,3,19,[23][24][25][26][27][28][29][30]. Several efficient methods have been proposed to solve this problem.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Infrastructure adaptation and emergence of loops in network routing with time-dependent loads

Lonardi¹,

Facca²,

Putti³

et al. 2021

Preprint

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Network routing approaches are widely used to study the evolution in time of self-adapting systems. However, few advances have been made for problems where adaptation is governed by time-dependent inputs. In this work, we study a dynamical systems where the edge conductivities-capacities-of a network are regulated by time-varying mass loads injected on nodes. Motivated by empirical observations, we assume that conductivities adapt slowly with respect to the characteristic time of the loads. Furthermore, assuming the loads to be periodic, we derive a new dynamics where the evolution of the system is governed by a matrix obtained with the Fourier coefficients of the input loads. Remarkably, we find a sufficient condition on these coefficients that determines when the resulting network topologies are trees. We show an example of this on the Bordeaux bus network where we tune the input loads to interpolate between loopy and tree topologies. We validate our model on several synthetic networks and provide an expression for long-time solutions of the original conductivities, supported by numerical observations and analytical arguments.

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Section: Discussionmentioning

confidence: 85%

Section: Conditions For the Generation Of Loops In Closed Formmentioning

confidence: 93%

“…Defining the complex vectors ν v = {c nv v } nv with entries the Fourier coefficients in (19), we rewrite…”

Section: Conditions For the Generation Of Loops In Closed Formmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Infrastructure adaptation and emergence of loops in network routing with time-dependent loads

Lonardi¹,

Facca²,

Putti³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

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Convergence properties of optimal transport-based temporal hypergraphs

Baptista

Bacco

2023

Appl Netw Sci

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We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of hypergraph structures. Discrete properties follow patterns that differ from those characterizing their continuous counterparts. Analyzing these patterns can bring new insights into the studied transportation principles. We also compare these higher-order structures to their network counterparts in terms of standard graph properties. We give evidence that some transportation schemes might benefit from hypernetwork representations. We demonstrate our method on real data by analyzing the properties of hypernetworks extracted from images of real systems.

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Multicommodity routing optimization for engineering networks

Lonardi

Putti

Bacco

2022

Sci Rep

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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 couple passengers’ fluxes by taking their sum or the sum of their squares. The first choice naturally reflects edges occupancy in transportation networks, however the second guarantees convergence to an optimal configuration of flows. Both modeling choices are applied to the Paris metro. 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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Convergence Properties of Optimal Transport-Based Temporal Networks

Cited by 6 publications

References 20 publications

Infrastructure adaptation and emergence of loops in network routing with time-dependent loads

Infrastructure adaptation and emergence of loops in network routing with time-dependent loads

Convergence properties of optimal transport-based temporal hypergraphs

Multicommodity routing optimization for engineering networks

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