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In this paper we study the min-cost flow problem in planar networks. We start with the min-cost flow problem and apply two transformations, one is based on geometric duality of planar graphs and the other on linear programming duality. The…
We introduce a general framework for flow problems over hypergraphs. In our problem formulation, which we call the convex flow problem, we have a concave utility function for the net flow at every node and a concave utility function for…
Traffic dynamics is universally crucial in analyzing and designing almost any network. This article introduces a novel theoretical approach to analyzing network traffic dynamics. This theory's machinery is based on the notion of traffic…
Efficiently solving large-scale optimal power flow (OPF) problems is challenging due to the high dimensionality and interconnectivity of modern power systems. Decomposition methods offer a promising solution via partitioning large problems…
Solving the power flow problem in a distributed fashion empowers different grid operators to compute the overall grid state without having to share grid models-this is a practical problem to which industry does not have off-the-shelf…
Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a…
Several high-throughput distributed data-processing applications require multi-hop processing of streams of data. These applications include continual processing on data streams originating from a network of sensors, composing a multimedia…
This paper investigates the behavior of the Min-Sum message passing scheme to solve systems of linear equations in the Laplacian matrices of graphs and to compute electric flows. Voltage and flow problems involve the minimization of…
Denoising-based models, including diffusion and flow matching, have led to substantial advances in graph generation. Despite this progress, such models remain constrained by two fundamental limitations: a computational cost that scales…
The solution of potential-driven steady-state flow in large networks is required in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear equations depends…
We link regularity and smoothness analysis of multivariate vector subdivision schemes with network flow theory and with special linear optimization problems. This connection allows us to prove the existence of what we call optimal…
We consider an optimal flow distribution problem in which the goal is to find a radial configuration that minimizes resistance-induced quadratic distribution costs while ensuring delivery of inputs from multiple sources to all sinks to meet…
Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cuts algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of…
In this paper we give an $\widetilde{O}((nm)^{2/3}\log C)$ time algorithm for computing min-cost flow (or min-cost circulation) in unit capacity planar multigraphs where edge costs are integers bounded by $C$. For planar multigraphs, this…
Distribution systems hold a very significant position in the power system since it is the main point of link between bulk power and consumers. A planned and effective distribution network is the key to cope up with the ever increasing…
This paper formalizes an optimal water-power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally…
In this paper, we present a novel learning framework for finding shortest paths in graphs utilizing Generative Flow Networks (GFlowNets). First, we examine theoretical properties of GFlowNets in non-acyclic environments in relation to…
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…
The traffic assignment problem is essential for traffic flow analysis, traditionally solved using mathematical programs under the Equilibrium principle. These methods become computationally prohibitive for large-scale networks due to…
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…