Related papers: Optimal Sequential Flows
We give an $O(n^{1.5}\log n)$ time algorithm for finding the maximum flow in a directed planar graph with multiple sources and a single sink. The techniques generalize to a subquadratic time algorithm for bounded genus graphs.
Formulating the alternating current optimal power flow (ACOPF) as a polynomial optimization problem makes it possible to solve large instances in practice and to guarantee asymptotic convergence in theory.
We derive a new parallel-in-time approach for solving large-scale optimization problems constrained by time-dependent partial differential equations arising from fluid dynamics. The solver involves the use of a block circulant approximation…
We consider the following inference problem: Given a set of edge-flow signals observed on a graph, lift the graph to a cell complex, such that the observed edge-flow signals can be represented as a sparse combination of gradient and curl…
In this work, we present a new approach to analyze the gradient flow for a positive semi-definite matrix denoising problem in an extensive-rank and high-dimensional regime. We use recent linear pencil techniques of random matrix theory to…
Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…
The degree sequence optimization problem is to find a subgraph of a given graph which maximizes the sum of given functions evaluated at the subgraph degrees. Here we study this problem by replacing degree sequences, via suitable nonlinear…
Many engineered systems, such as energy and transportation infrastructures, are networks governed by non-linear physical laws. A primary challenge for operators of these networks is to achieve optimal utilization while maintaining safety…
We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…
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…
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…
We present elements of a typing theory for flow networks, where "types", "typings", and "type inference" are formulated in terms of familiar notions from polyhedral analysis and convex optimization. Based on this typing theory, we develop…
Among the models of quantum computation, the One-way Quantum Computer is one of the most promising proposals of physical realization, and opens new perspectives for parallelization by taking advantage of quantum entanglement. Since a…
This paper introduces a novel theoretical framework and a suite of highly efficient, parallelizable algorithms for solving the large-scale multicommodity flow (MCF) feasibility problem. We reframe the classical constraint-satisfaction…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
Optimal power flow (OPF) is a critical optimization problem that allocates power to the generators in order to satisfy the demand at a minimum cost. Solving this problem exactly is computationally infeasible in the general case. In this…
We present faster algorithms for approximate maximum flow in undirected graphs with good separator structures, such as bounded genus, minor free, and geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a recursive…
An improved fully polynomial-time approximation scheme and a greedy heuristic for the fractional length-bounded maximum multicommodity flow problem with unit edge-lengths are proposed. Computational experiments are carried out on benchmark…
In this paper we show an O(n^(3/2) log^2 n) time algorithm for finding a maximum flow in a planar graph with multiple sources and multiple sinks. This is the fastest algorithm whose running time depends only on the number of vertices in the…
In this paper we present an O(n log n) algorithm for finding a maximum flow in a directed planar graph, where the vertices are subject to capacity constraints, in addition to the arcs. If the source and the sink are on the same face, then…