Related papers: Water transport on finite graphs
If the nodes of a graph are considered to be identical barrels - featuring different water levels - and the edges to be (locked) water-filled pipes in between the barrels, one might consider the optimization problem of how much the water…
If the nodes of a graph are considered to be identical barrels - featuring different water levels - and the edges to be (locked) water-filled pipes in between the barrels, consider the optimization problem of how much the water level in a…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
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…
Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…
Optimizing embedded systems, where the optimization of one depends on the state of another, is a formidable computational and algorithmic challenge, that is ubiquitous in real world systems. We study flow networks, where bilevel…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
In many urban areas of the developing world, piped water is supplied only intermittently, as valves direct water to different parts of the water distribution system at different times. The flow is transient, and may transition between…
Recent advances in dynamic graph processing have enabled the analysis of highly dynamic graphs with change at rates as high as millions of edge changes per second. Solutions in this domain, however, have been demonstrated only for…
Branched Optimal Transport (BOT) is a generalization of optimal transport in which transportation costs along an edge are subadditive. This subadditivity models an increase in transport efficiency when shipping mass along the same route,…
I introduce a new approach to the maximum flow problem by a simple algorithm with a slightly better runtime. This approach is based on sorting arcs insight of vertices on a residual graph. This new approach leads to an O(mn^0.5) time bound…
Numerous networks, such as transportation, distribution and delivery networks optimize their designs in order to increase efficiency and lower costs, improving the stability of its intended functions, etc. Networks that distribute goods,…
The vitality of an edge in a graph with respect to the maximum flow between two fixed vertices $s$ and $t$ is defined as the reduction of the maximum flow value caused by the removal of that edge. The max-flow vitality problem has already…
There are well-established connections between combinatorial optimization, optimal transport theory and Hydrodynamics, through the linear assignment problem in combinatorics, the Monge-Kantorovich problem in optimal transport theory and the…
The minimum cost-flow problems have been attracted recently in optimization because of their applications in several areas of applied science and real life. Therefore, finding optima solution of these problems would be significant. Although…
It is shown that optimal network plans can be obtained, naturally, as a limit of easier problems of point allocations. These problems are obtained by minimizing the mass transportation on the set of atomic measures of prescribed number of…
We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for…
The branched transport problem, a popular recent variant of optimal transport, is a non-convex and non-smooth variational problem on Radon measures. The so-called urban planning problem, on the contrary, is a shape optimization problem that…
Many situations in physics, biology, and engineering consist of the transport of some physical quantity through a network of narrow channels. The ability of a network to transport such a quantity in every direction can be described by the…