相关论文: Towards (1+\epsilon)-Approximate Flow Sparsifiers

We introduce a new approach to the maximum flow problem in undirected, capacitated graphs using $\alpha$-\emph{congestion-approximators}: easy-to-compute functions that approximate the congestion required to route single-commodity demands…

Length-constrained expander decompositions are a new graph decomposition that has led to several recent breakthroughs in fast graph algorithms. Roughly, an $(h, s)$-length $\phi$-expander decomposition is a small collection of length…

We introduce the Flow Stochastic Segmentation Network (Flow-SSN), a generative segmentation model family featuring discrete-time autoregressive and modern continuous-time flow variants. We prove fundamental limitations of the low-rank…

Continuing from Part 1 (Hern\'andez \emph{et al.}, \emph{arXiv:2108.12395}, 2021), a generalized quasilinear (GQL) approximation is studied in turbulent channel flow using a flow decomposition defined with spanwise Fourier modes: the flow…

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…

We consider communication-efficient weighted and unweighted (uniform) random sampling from distributed data streams presented as a sequence of mini-batches of items. This is a natural model for distributed streaming computation, and our…

Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…

Time-Triggered Communication is a key technology for many safety-critical systems, with applications spanning the areas of aerospace and industrial control. Such communication relies on time-triggered flows, with each flow consisting of…

We present a novel asymptotic-preserving semi-implicit finite element method for weakly compressible and incompressible flows based on compatible finite element spaces. The momentum is sought in an $H(\mathrm{div})$-conforming space,…

In the Network Flow Interdiction problem an adversary attacks a network in order to minimize the maximum s-t-flow. Very little is known about the approximatibility of this problem despite decades of interest in it. We present the first…

Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used in machine learning over homogeneous graphs. In heterogeneous graphs such as knowledge graphs, however, sparsification has not been systematically…

In the almost-everywhere reliable message transmission problem, introduced by [Dwork, Pippenger, Peleg, Upfal'86], the goal is to design a sparse communication network $G$ that supports efficient, fault-tolerant protocols for interactions…

In optical flow estimation task, coarse-to-fine (C2F) warping strategy is widely used to deal with the large displacement problem and provides efficiency and speed. However, limited by the small search range between the first images and…

Training large neural networks is time consuming. To speed up the process, distributed training is often used. One of the largest bottlenecks in distributed training is communicating gradients across different nodes. Different gradient…

In this paper, we study the generalized multiscale finite element method (GMsFEM) for single phase compressible flow in highly heterogeneous porous media. We follow the major steps of the GMsFEM to construct permeability dependent offline…

Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the…

Given an $n$-vertex non-negatively real-weighted graph $G$, whose vertices are partitioned into a set of $k$ clusters, a \emph{clustered network design problem} on $G$ consists of solving a given network design optimization problem on $G$,…

Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…

Hypergraphs allow modeling problems with multi-way high-order relationships. However, the computational cost of most existing hypergraph-based algorithms can be heavily dependent upon the input hypergraph sizes. To address the…

Data-flow analyses usually associate information with control flow regions. Informally, if these regions are too small, like a point between two consecutive statements, we call the analysis dense. On the other hand, if these regions include…