Related papers: Brief Announcement: Almost-Tight Approximation Dis…
We study the problem of computing the minimum cut in a weighted distributed message-passing networks (the CONGEST model). Let $\lambda$ be the minimum cut, $n$ be the number of nodes in the network, and $D$ be the network diameter. Our…
In this paper, we study the problem of approximating the minimum cut in a distributed message-passing model, the CONGEST model. The minimum cut problem has been well-studied in the context of centralized algorithms. However, there were no…
We study the problem of computing approximate minimum edge cuts by distributed algorithms. We use a standard synchronous message passing model where in each round, $O(\log n)$ bits can be transmitted over each edge (a.k.a. the CONGEST…
Minimum-weight cut (min-cut) is a basic measure of a network's connectivity strength. While the min-cut can be computed efficiently in the sequential setting [Karger STOC'96], there was no efficient way for a distributed network to compute…
We present near-optimal algorithms for detecting small vertex cuts in the CONGEST model of distributed computing. Despite extensive research in this area, our understanding of the vertex connectivity of a graph is still incomplete,…
We present new distributed algorithms for constructing a Steiner Forest in the CONGEST model. Our deterministic algorithm finds, for any given constant $\epsilon>0$, a $(2+\epsilon)$-approximation in $\tilde{O}(sk+\sqrt{\min(st,n)})$…
Finding sparse cuts is an important tool in analyzing large-scale distributed networks such as the Internet and Peer-to-Peer networks, as well as large-scale graphs such as the web graph, online social communities, and VLSI circuits. In…
We present the first sublinear-time algorithm for a distributed message-passing network sto compute its edge connectivity $\lambda$ exactly in the CONGEST model, as long as there are no parallel edges. Our algorithm takes $\tilde…
We present an algorithm for distributed networks to efficiently find a small vertex cut in the CONGEST model. Given a positive integer $\kappa$, our algorithm can, with high probability, either find $\kappa$ vertices whose removal…
We present a universally-optimal distributed algorithm for the exact weighted min-cut. The algorithm is guaranteed to complete in $\widetilde{O}(D + \sqrt{n})$ rounds on every graph, recovering the recent result of Dory, Efron,…
A long series of recent results and breakthroughs have led to faster and better distributed approximation algorithms for single source shortest paths (SSSP) and related problems in the CONGEST model. The runtime of all these algorithms,…
In this thesis, we present fast deterministic algorithm to find small cuts in distributed networks. Finding small min-cuts for a network is essential for ensuring the quality of service and reliability. Throughout this thesis, we use the…
We present a deterministic $(1+o(1))$-approximation $(n^{1/2+o(1)}+D^{1+o(1)})$-time algorithm for solving the single-source shortest paths problem on distributed weighted networks (the CONGEST model); here $n$ is the number of nodes in the…
We give almost-linear-time algorithms for approximating rooted minimum cut and maximum arborescence packing in directed graphs, two problems that are dual to each other [Edm73]. More specifically, for an $n$-vertex, $m$-edge directed graph…
Distributed network optimization algorithms, such as minimum spanning tree, minimum cut, and shortest path, are an active research area in distributed computing. This paper presents a fast distributed algorithm for such problems in the…
A singularly (near) optimal distributed algorithm is one that is (near) optimal in \emph{two} criteria, namely, its time and message complexities. For \emph{synchronous} CONGEST networks, such algorithms are known for fundamental…
We provide a simple new randomized contraction approach to the global minimum cut problem for simple undirected graphs. The contractions exploit 2-out edge sampling from each vertex rather than the standard uniform edge sampling. We…
In the {\em distributed all-pairs shortest paths} problem (APSP), every node in the weighted undirected distributed network (the CONGEST model) needs to know the distance from every other node using least number of communication rounds…
We present randomized algorithms that compute $(1+\epsilon)$-approximate minimum global edge and vertex cuts in weighted directed graphs in $O(\log^4(n) / \epsilon)$ and $O(\log^5(n)/\epsilon)$ single-commodity flows, respectively. With the…
We present a near-optimal distributed algorithm for $(1+o(1))$-approximation of single-commodity maximum flow in undirected weighted networks that runs in $(D+ \sqrt{n})\cdot n^{o(1)}$ communication rounds in the \Congest model. Here, $n$…