Related papers: A Simple Deterministic Distributed MST Algorithm, …
The minimum-cost $k$-edge-connected spanning subgraph ($k$-ECSS) problem is a generalization and strengthening of the well-studied minimum-cost spanning tree (MST) problem. While the round complexity of distributedly computing the latter…
We study the {\em verification} problem in distributed networks, stated as follows. Let $H$ be a subgraph of a network $G$ where each vertex of $G$ knows which edges incident on it are in $H$. We would like to verify whether $H$ has some…
We study deterministic algorithms for computing graph cuts, with focus on two fundamental problems: balanced sparse cut and $k$-vertex connectivity for small $k$ ($k=O(\polylog n)$). Both problems can be solved in near-linear time with…
We give a deterministic algorithm for finding the minimum (weight) cut of an undirected graph on $n$ vertices and $m$ edges using $\text{polylog}(n)$ calls to any maximum flow subroutine. Using the current best deterministic maximum flow…
Directed Steiner Tree (DST) is a central problem in combinatorial optimization and theoretical computer science: Given a directed graph $G=(V, E)$ with edge costs $c \in \mathbb{R}_{\geq 0}^E$, a root $r \in V$ and $k$ terminals $K\subseteq…
Memory-(in)efficiency is a crucial consideration that oftentimes prevents deployment of state-of-the-art distributed algorithms in real-life modern networks. In the context of the MST problem, roughly speaking, there are three types of…
In this paper, we study a survivable network design problem on directed graphs, 2-Connected Directed Steiner Tree (2-DST): given an $n$-vertex weighted directed graph, a root $r$, and a set of $h$ terminals $S$, find a min-cost subgraph $H$…
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…
In the Directed Steiner Tree (DST) problem we are given an $n$-vertex directed edge-weighted graph, a root $r$, and a collection of $k$ terminal nodes. Our goal is to find a minimum-cost arborescence that contains a directed path from $r$…
Finding a minimum spanning tree (MST) for $n$ points in an arbitrary metric space is a fundamental primitive for hierarchical clustering and many other ML tasks, but this takes $\Omega(n^2)$ time to even approximate. We introduce a…
In this short paper, we present an improved algorithm for approximating the minimum cut on distributed (CONGEST) networks. Let $\lambda$ be the minimum cut. Our algorithm can compute $\lambda$ exactly in…
The distributed single-source shortest paths problem is one of the most fundamental and central problems in the message-passing distributed computing. Classical Bellman-Ford algorithm solves it in $O(n)$ time, where $n$ is the number of…
We present a novel self-stabilizing algorithm for minimum spanning tree (MST) construction. The space complexity of our solution is $O(\log^2n)$ bits and it converges in $O(n^2)$ rounds. Thus, this algorithm improves the convergence time of…
The \emph{Steiner tree} problem is one of the fundamental and classical problems in combinatorial optimization. In this paper, we study this problem in the $\mathcal{CONGESTED}$ $\mathcal{CLIQUE}$ model of distributed computing and present…
This paper demonstrates the usefulness of distributed local verification of proofs, as a tool for the design of self-stabilizing algorithms.In particular, it introduces a somewhat generalized notion of distributed local proofs, and utilizes…
In this paper we present and evaluate a parallel algorithm for solving a minimum spanning tree (MST) problem for supercomputers with distributed memory. The algorithm relies on the relaxation of the message processing order requirement for…
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…
Given a distributed network represented by a weighted undirected graph $G=(V,E)$ on $n$ vertices, and a parameter $k$, we devise a distributed algorithm that computes a routing scheme in $(n^{1/2+1/k}+D)\cdot n^{o(1)}$ rounds, where $D$ is…
It has been shown that one can design distributed algorithms that are (nearly) singularly optimal, meaning they simultaneously achieve optimal time and message complexity (within polylogarithmic factors), for several fundamental global…
The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques…