Related papers: Flow Metrics on Graphs
Fluid transport networks are important in many natural settings and engineering applications, from animal cardiovascular and respiratory systems to plant vasculature to plumbing networks and chemical plants. Understanding how network…
Complex systems of interacting components often can be modeled by a simple graph $\mathcal{G}$ that consists of a set of $n$ nodes and a set of $m$ edges. Such a graph can be represented by an adjacency matrix $A\in\R^{n\times n}$, whose…
The minimum cost flow problem is one of the most studied network optimization problems and appears in numerous applications. Some efficient algorithms exist for this problem, which are freely available in the form of libraries or software…
In this paper, we study two applications of graph minor reduction. In the first part of the paper, we introduce a variant of the boxicity, called strong boxicity, where the rectangular representation satisfies an additional condition that…
In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…
This paper focuses on network resilience to perturbation of edge weight. Other than connectivity, many network applications nowadays rely upon some measure of network distance between a pair of connected nodes. In these systems, a metric…
We present an $m^{4/3+o(1)}\log W$-time algorithm for solving the minimum cost flow problem in graphs with unit capacity, where $W$ is the maximum absolute value of any edge weight. For sparse graphs, this improves over the best known…
Graphs are versatile tools for representing structured data. As a result, a variety of machine learning methods have been studied for graph data analysis. Although many such learning methods depend on the measurement of differences between…
In contrast to traditional flow networks, in additive flow networks, to every edge e is assigned a gain factor g(e) which represents the loss or gain of the flow while using edge e. Hence, if a flow f(e) enters the edge e and f(e) is less…
We consider the fundamental algorithmic problem of finding a cycle of minimum weight in a weighted graph. In particular, we show that the minimum weight cycle problem in an undirected n-node graph with edge weights in {1,...,M} or in a…
We show a fast algorithm for determining the set of edges in a planar undirected unweighted graph, whose deletion reduces the maximum flow between two fixed vertices. This is a special case of the max flow vitality problem, that has been…
As the popularity of graph data increases, there is a growing need to count the occurrences of subgraph patterns of interest, for a variety of applications. Many graphs are massive in scale and also fully dynamic (with insertions and…
We improve on random sampling techniques for approximately solving problems that involve cuts and flows in graphs. We give a near-linear-time construction that transforms any graph on n vertices into an O(n\log n)-edge graph on the same…
We introduce a methodology to study the possible matter flows of an ecosystem defined by observational biomass data and realistic biological constraints. The flows belong to a polyhedron in a multi dimensional space making statistical…
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…
We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average…
This paper investigates the connections between rectified flows, flow matching, and optimal transport. Flow matching is a recent approach to learning generative models by estimating velocity fields that guide transformations from a source…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
This paper addresses the challenges of evaluating network performance in the presence of fluctuating traffic patterns, with a particular focus on the impact of peak data rates on network resources. We introduce a set of metrics to quantify…