Related papers: Exact Flow Sparsification Requires Unbounded Size
We give almost-linear-time algorithms for constructing sparsifiers with $n\ poly(\log n)$ edges that approximately preserve weighted $(\ell^{2}_2 + \ell^{p}_p)$ flow or voltage objectives on graphs. For flow objectives, this is the first…
Data is said to follow the transform (or analysis) sparsity model if it becomes sparse when acted on by a linear operator called a sparsifying transform. Several algorithms have been designed to learn such a transform directly from data,…
A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of…
We introduce the Unsplittable Transshipment Problem in directed graphs with multiple sources and sinks. An unsplittable transshipment routes given supplies and demands using at most one path for each source-sink pair. Although they are a…
The traditional multi-commodity flow problem assumes a given flow network in which multiple commodities are to be maximally routed in response to given demands. This paper considers the multi-commodity flow network-design problem: given a…
Flow over a surface can be stratified by imposing a fixed mean vertical temperature (density) gradient profile throughout or via cooling at the surface. These distinct mechanisms can act simultaneously to establish a stable stratification…
We consider the problem of finding a feasible single-commodity flow in a strongly connected network with fixed supplies and demands, provided that the sum of supplies equals the sum of demands and the minimum arc capacity is at least this…
Given a graph with non-negative edge weights, there are various ways to interpret the edge weights and induce a metric on the vertices of the graph. A few examples are shortest-path, when interpreting the weights as lengths; resistance…
In the Flow Edge-Monitor Problem, we are given an undirected graph G=(V,E), an integer k > 0 and some unknown circulation \psi on G. We want to find a set of k edges in G, so that if we place k monitors on those edges to measure the flow…
Flow Matching has recently emerged as a popular class of generative models for simulating a target distribution $\mu_1$ from samples drawn from a source distribution $\mu_0$. This framework relies on a fixed coupling between $\mu_0$ and…
In this paper, we study fractional multiflows in undirected graphs. A fractional multiflow in a graph G with a node subset T, called terminals, is a collection of weighted paths with ends in T such that the total weights of paths traversing…
We consider a network design problem called the generalized terminal backup problem. Whereas earlier work investigated the edge-connectivity constraints only, we consider both edge- and node-connectivity constraints for this problem. A…
The max-flow outer bound is achievable by regenerating codes for functional repair distributed storage system. However, the capacity of exact repair distributed storage system is an open problem. In this paper, the linear programming bound…
In this paper we initiate the study of expander decompositions of a graph $G=(V, E)$ in the streaming model of computation. The goal is to find a partitioning $\mathcal{C}$ of vertices $V$ such that the subgraphs of $G$ induced by the…
Recent works have established the utility of sparsity-promoting norms for extracting spatially-localized instability mechanisms in fluid flows, with possible implications for flow control. However, these prior works have focused on linear…
We introduce a new algorithmic framework for designing dynamic graph algorithms in minor-free graphs, by exploiting the structure of such graphs and a tool called vertex sparsification, which is a way to compress large graphs into small…
The terminal backup problems (Anshelevich and Karagiozova (2011)) form a class of network design problems: Given an undirected graph with a requirement on terminals, the goal is to find a minimum cost subgraph satisfying the connectivity…
An extended formulation of a polytope is a linear description of this polytope using extra variables besides the variables in which the polytope is defined. The interest of extended formulations is due to the fact that many interesting…
We study \emph{dynamic} algorithms for maintaining spectral vertex sparsifiers of graphs with respect to a set of terminals $T$ of our choice. Such objects preserve pairwise resistances, solutions to systems of linear equations, and energy…
We introduce Tiered Sampling, a novel technique for approximate counting sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size $M$, which…