Related papers: Minimum-weight Spanning Tree Construction in $O(\l…
We design fast deterministic algorithms for distance computation in the congested clique model. Our key contributions include: -- A $(2+\epsilon)$-approximation for all-pairs shortest paths in $O(\log^2{n} / \epsilon)$ rounds on unweighted…
In this paper, we present a new randomized $O(1)$-approximation algorithm for the All-Pairs Shortest Paths (APSP) problem in weighted undirected graphs that runs in just $O(\log \log \log n)$ rounds in the Congested-Clique model. Before our…
We consider a family of local search algorithms for the minimum-weight spanning tree, indexed by a parameter $\rho$. One step of the local search corresponds to replacing a connected induced subgraph of the current candidate graph whose…
Distributed graph algorithms that separately optimize for either the number of rounds used or the total number of messages sent have been studied extensively. However, algorithms simultaneously efficient with respect to both measures have…
The minimal spanning tree (MST) algorithm is a graph-theoretical cluster-finding method. We previously applied it to gamma-ray bidimensional images, showing that it is quite sensitive in finding faint sources. Possible sources are…
The minimum spanning tree (MST) construction is a classical problem in Distributed Computing for creating a globally minimized structure distributedly. Self-stabilization is versatile technique for forward recovery that permits to handle…
The minimum-weight $2$-edge-connected spanning subgraph (2-ECSS) problem is a natural generalization of the well-studied minimum-weight spanning tree (MST) problem, and it has received considerable attention in the area of network design.…
Bounded-angle (minimum) spanning trees were first introduced in the context of wireless networks with directional antennas. They are reminiscent of bounded-degree spanning trees, which have received significant attention. Let $P =…
In this paper, we study weakly dynamic undirected graphs, that can be used to represent some logistic networks. The goal is to deliver all the delivery points in the network. The network exists in a mostly stable environment, except for a…
In this lecture we will consider the minimum weight spanning tree (MST) problem, i.e., one of the simplest and most vital combinatorial optimization problems. We will discuss a particular greedy algorithm that allows to compute a MST for…
In the context of algorithm theory, various studies have been conducted on spanning trees with desirable properties. In this paper, we consider the \textsc{Minimum Cover Spanning Tree} problem (MCST for short). Given a graph $G$ and a…
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…
Minimum spanning trees (MSTs) provide a convenient representation of datasets in numerous pattern recognition activities. Moreover, they are relatively fast to compute. In this paper, we quantify the extent to which they are meaningful in…
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…
This paper studies constructive heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree that uses edges that are as similar as possible. Given an undirected labeled connected graph (i.e.,…
We present a uniform self-stabilizing algorithm, which solves the problem of distributively finding a minimum diameter spanning tree of an arbitrary positively real-weighted graph. Our algorithm consists in two stages of stabilizing…
In this paper the minimum spanning tree problem with uncertain edge costs is discussed. In order to model the uncertainty a discrete scenario set is specified and a robust framework is adopted to choose a solution. The min-max, min-max…
The semi-streaming model is a variant of the streaming model frequently used for the computation of graph problems. It allows the edges of an $n$-node input graph to be read sequentially in $p$ passes using $\tilde{O}(n)$ space. In this…
In this paper, we consider the minimum spanning tree problem (for short, MSTP) on an arbitrary set of $n$ points of $d$-dimensional space in $l_1$-norm. For this problem, for each fixed $d\geq 2$, there is a known algorithm of the…
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…