Related papers: Flow Metrics on Graphs
Minimum flow decomposition (MFD) is the NP-hard problem of finding a smallest decomposition of a network flow/circulation $X$ on a directed graph $G$ into weighted source-to-sink paths whose superposition equals $X$. We show that, for…
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…
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 present an algebraic approach to the watershed adapted to edge or node weighted graphs. Starting with the flooding adjunction, we introduce the flooding graphs, for which node and edge weights may be deduced one from the other. Each node…
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…
Flow velocity is an important characteristic of the fluidic mediums. In this paper, we introduce a molecular based flow velocity meter consisting of a molecule releasing node and a receiver that counts these molecules. We consider both flow…
Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…
Many real-world phenomena are best represented as interaction networks with dynamic structures (e.g., transaction networks, social networks, traffic networks). Interaction networks capture flow of data which is transferred between their…
We investigate how the underlying graph of a network supports a flow between a source node and a destination node and propose to compute the expected number of nodes and links that contribute to transferring items in random graphs. Since…
Flow sparsification is a classic graph compression technique which, given a capacitated graph $G$ on $k$ terminals, aims to construct another capacitated graph $H$, called a flow sparsifier, that preserves, either exactly or approximately,…
We study evolution equations on metric graphs with reservoirs, that is graphs where a one-dimensional interval is associated to each edge and, in addition, the vertices are able to store and exchange mass with these intervals. Focusing on…
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…
In this paper we study minimum cut and maximum flow problems on planar graphs, both in static and in dynamic settings. First, we present an algorithm that given an undirected planar graph computes the minimum cut between any two given…
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…
We consider network models where information items flow %are sent from a source to a sink node. We start with a model where routing is constrained by energy available on nodes in finite supply (like in Smartdust) and efficiency is related…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
In this paper, we introduce the solver ConvexFlows for the convex flow problem first defined in the authors' previous work. In this problem, we aim to optimize a concave utility function depending on the flows over a graph. However, unlike…
We give the first almost-linear total time algorithm for deciding if a flow of cost at most $F$ still exists in a directed graph, with edge costs and capacities, undergoing decremental updates, i.e., edge deletions, capacity decreases, and…
Analyzing massive data sets has been one of the key motivations for studying streaming algorithms. In recent years, there has been significant progress in analysing distributions in a streaming setting, but the progress on graph problems…
Physical Flow Networks are different infrastructure networks that allow the flow of physical commodities through edges between its constituent nodes. These include power grid, natural gas transmission network, water pipelines etc. In such…