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Several concepts borrowed from graph theory are routinely used to better understand the inner workings of the (human) brain. To this end, a connectivity network of the brain is built first, which then allows one to assess quantities such as…
The sequential nature of autoregressive next-token prediction imposes a fundamental speed limit on large language models. While continuous flow models offer a path to parallel generation, they traditionally demand expensive iterative…
In this paper we provide an algorithm which given any $m$-edge $n$-vertex directed graph with integer capacities at most $U$ computes a maximum $s$-$t$ flow for any vertices $s$ and $t$ in $m^{11/8+o(1)}U^{1/4}$ time with high probability.…
We provide an algorithm which, with high probability, maintains a $(1-\epsilon)$-approximate maximum flow on an undirected graph undergoing $m$-edge additions in amortized $m^{o(1)} \epsilon^{-3}$ time per update. To obtain this result, we…
Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cuts algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of…
We consider the Minimum Multi-Commodity Flow Subgraph (MMCFS) problem: given a directed graph $G$ with edge capacities $\mathit{cap}$ and a retention ratio $\alpha\in(0,1)$, find an edge-wise minimum subgraph $G' \subseteq G$ such that for…
In this paper, we introduce a new framework for approximately solving flow problems in capacitated, undirected graphs and apply it to provide asymptotically faster algorithms for the maximum $s$-$t$ flow and maximum concurrent…
We present a parallel algorithm for the $(1-\epsilon)$-approximate maximum flow problem in capacitated, undirected graphs with $n$ vertices and $m$ edges, achieving $O(\epsilon^{-3}\text{polylog} n)$ depth and $O(m \epsilon^{-3}…
Networks of interconnected resistors, springs and beams, or pores are standard models of studying scalar and vector transport processes in heterogeneous materials and media, such as fluid flow in porous media, and conduction, deformations,…
This paper introduces a framework for solving alternating current optimal power flow (ACOPF) problems using graphics processing units (GPUs). While GPUs have demonstrated remarkable performance in various computing domains, their…
Shape priors have been widely utilized in medical image segmentation to improve segmentation accuracy and robustness. A major way to encode such a prior shape model is to use a mesh representation, which is prone to causing…
We initiate the study of graph algorithms in the streaming setting on massive distributed and parallel systems inspired by practical data processing systems. The objective is to design algorithms that can efficiently process evolving graphs…
In this paper we provide an algorithm for maintaining a $(1-\epsilon)$-approximate maximum flow in a dynamic, capacitated graph undergoing edge additions. Over a sequence of $m$-additions to an $n$-node graph where every edge has capacity…
Execution graphs of parallel loop programs exhibit a nested, repeating structure. We show how such graphs that are the result of nested repetition can be represented by succinct parametric structures. This parametric graph template…
We investigate the dependence of the approximation capacity of deep residual networks on its depth in a continuous dynamical systems setting. This can be formulated as the general problem of quantifying the minimal time-horizon required to…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
Rapid advances in image acquisition and storage technology underline the need for algorithms that are capable of solving large scale image processing and computer-vision problems. The minimum cut problem plays an important role in…
We investigate the time-complexity of the All-Pairs Max-Flow problem: Given a graph with $n$ nodes and $m$ edges, compute for all pairs of nodes the maximum-flow value between them. If Max-Flow (the version with a given source-sink pair…
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…
We prove an approximate max-multiflow min-multicut theorem for bounded treewidth graphs. In particular, we show the following: Given a treewidth-$r$ graph, there exists a (fractional) multicommodity flow of value $f$, and a multicut of…