Related papers: Water transport on finite graphs
Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…
Natural gas consumption by users of pipeline networks is subject to increasing uncertainty that originates from the intermittent nature of electric power loads serviced by gas-fired generators. To enable computationally efficient…
Stream graphs model highly dynamic networks in which nodes and/or links arrive and/or leave over time. Strongly connected components in stream graphs were defined recently, but no algorithm was provided to compute them. We present here…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
We study biplane graphs drawn on a finite planar point set $S$ in general position. This is the family of geometric graphs whose vertex set is $S$ and can be decomposed into two plane graphs. We show that two maximal biplane graphs---in the…
The basic optimal transportation problem consists in finding the most effective way of moving masses from one location to another, while minimizing the transportation cost. Such concept has been found to be useful to understand various…
In this paper, we present a neural network approach to address the dynamic unbalanced optimal transport problem on surfaces with point cloud representation. For surfaces with point cloud representation, traditional method is difficult to…
We give an algorithm that computes exact maximum flows and minimum-cost flows on directed graphs with $m$ edges and polynomially bounded integral demands, costs, and capacities in $m^{1+o(1)}$ time. Our algorithm builds the flow through a…
Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the…
We give an iterative algorithm for finding the maximum flow between a set of sources and sinks that lie on the boundary of a planar graph. Our algorithm uses only O(n) queries to simple data structures, achieving an O(n log n) running time…
We propose a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely…
Network optimization has generally been focused on solving network flow problems, but recently there have been investigations into optimizing network characteristics. Optimizing network connectivity to maximize the number of nodes within a…
Connectivity (or equivalently, unweighted maximum flow) is an important measure in graph theory and combinatorial optimization. Given a graph $G$ with vertices $s$ and $t$, the connectivity $\lambda(s,t)$ from $s$ to $t$ is defined to be…
We consider ordinal approximation algorithms for a broad class of utility maximization problems for multi-agent systems. In these problems, agents have utilities for connecting to each other, and the goal is to compute a maximum-utility…
We propose a numerical method to find the optimal transport map between a measure supported on a lower-dimensional subset of R^d and a finitely supported measure. More precisely, the source measure is assumed to be supported on a simplex…
We consider transport in a fluid flow of arbitrary complexity but with a dominant flow direction. This is the situation encountered, for example, when analyzing the dynamics of sufficiently small particles immersed in a turbulent fluid and…
Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…
We take a new look at the relation between the optimal transport problem and the Schr\"{o}dinger bridge problem from the stochastic control perspective. We show that the connections are richer and deeper than described in existing…
We consider the classic maximal and maximum independent set problems in three models of graph streams: In the edge-arrival model we see a stream of edges which collectively define a graph, this model has been well-studied for a variety of…