Related papers: A Nearly Time-Optimal Distributed Approximation of…
We consider the Minimum-$(k,\rho)$-$\mathrm{Shortcut}$ problem ($\min(k,\rho)\text{-}\mathrm{Shortcut}$), where the goal is to find the smallest set of shortcut edges such that every vertex in a given graph can reach its $\rho$ closest…
The Strongly Connected Steiner Subgraph (SCSS) problem is a well-studied network design problem that asks for a minimum subgraph that strongly connects a given set of terminals. In this paper, we present several new algorithmic and…
The node-averaged complexity of a distributed algorithm running on a graph $G=(V,E)$ is the average over the times at which the nodes $V$ of $G$ finish their computation and commit to their outputs. We study the node-averaged complexity for…
This work presents a maximum entropy principle based algorithm for solving minimum multiway $k$-cut problem defined over static and dynamic {\em digraphs}. A multiway $k$-cut problem requires partitioning the set of nodes in a graph into…
Given an edge-weighted directed graph $G=(V,E)$ on $n$ vertices and a set $T=\{t_1, t_2, \ldots, t_p\}$ of $p$ terminals, the objective of the \scss ($p$-SCSS) problem is to find an edge set $H\subseteq E$ of minimum weight such that $G[H]$…
We provide a comprehensive study of a natural geometric optimization problem motivated by questions in the context of satellite communication and astrophysics. In the problem Minimum Scan Cover with Angular Costs (MSC), we are given a graph…
We investigate a process of joining $k$ random spanning trees on a fixed clique $K_n$. The joined trees may not be disjoint and multiple edges are replaced by one simple edge. This process produces a simple graph $G$ on $n$~vertices with an…
We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is…
Over the past decade, there has been increasing interest in distributed/parallel algorithms for processing large-scale graphs. By now, we have quite fast algorithms -- usually sublogarithmic-time and often $poly(\log\log n)$-time, or even…
The Directed Steiner Network (DSN) problem takes as input a directed edge-weighted graph $G=(V,E)$ and a set $\mathcal{D}\subseteq V\times V$ of $k$ demand pairs. The aim is to compute the cheapest network $N\subseteq G$ for which there is…
The $k$-center problem is a central optimization problem with numerous applications for machine learning, data mining, and communication networks. Despite extensive study in various scenarios, it surprisingly has not been thoroughly…
In the $k$-cut problem, we want to find the lowest-weight set of edges whose deletion breaks a given (multi)graph into $k$ connected components. Algorithms of Karger \& Stein can solve this in roughly $O(n^{2k})$ time. On the other hand,…
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…
We consider the problem of designing sublinear time algorithms for estimating the cost of a minimum metric traveling salesman (TSP) tour. Specifically, given access to a $n \times n$ distance matrix $D$ that specifies pairwise distances…
We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: - We give a greedy algorithm…
Let $T=(V,E)$ be a tree with associated costs on its subtrees. A minmax $k$-partition of $T$ is a partition into $k$ subtrees, minimizing the maximum cost of a subtree over all possible partitions. In the centered version of the problem,…
Building a spanning tree, minimum spanning tree (MST), and BFS tree in a distributed network are fundamental problems which are still not fully understood in terms of time and communication cost. x The first work to succeed in computing a…
We consider the densest $k$-subgraph problem, which seeks to identify the $k$-node subgraph of a given input graph with maximum number of edges. This problem is well-known to be NP-hard, by reduction to the maximum clique problem. We…
In the {\sc Min-Sum 2-Clustering} problem, we are given a graph and a parameter $k$, and the goal is to determine if there exists a 2-partition of the vertex set such that the total conflict number is at most $k$, where the conflict number…
We investigate the \emph{minimum weight cycle (MWC)} problem in the $\mathsf{CONGEST}$ model of distributed computing. For undirected weighted graphs, we design a randomized algorithm that achieves a $(k+1)$-approximation, for any…