Related papers: Solving the minimum labelling spanning tree proble…
A quadratic minimum spanning tree (QMST) problem is to determine a minimum spanning tree of a connected graph having edges which are associated with linear and quadratic weights. The linear weights are the edge costs which are associated…
This paper presents a randomized Las Vegas distributed algorithm that constructs a minimum spanning tree (MST) in weighted networks with optimal (up to polylogarithmic factors) time and message complexity. This algorithm runs in…
The quadratic minimum spanning tree problem (QMSTP) is the problem of finding a spanning tree of a graph such that the total interaction cost between pairs of edges in the tree is minimized. We first show that most of the bounding…
There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest and most frequently used draw random weights on the edges…
In real life, it is always an urge to reach our goal in minimum effort i.e., it should have a minimum constrained path. The path may be shortest route in practical life, either physical or electronic medium. The scenario is to represents…
Network interdiction problems are a natural way to study the sensitivity of a network optimization problem with respect to the removal of a limited set of edges or vertices. One of the oldest and best-studied interdiction problems is…
A labelled, undirected graph is a graph whose edges have assigned labels, from a specific set. Given a labelled, undirected graph, the well-known minimum labelling spanning tree problem is aimed at finding the spanning tree of the graph…
In this paper, we present a fully-dynamic distributed algorithm for maintaining a minimum spanning tree on general graphs with positive real edge weights. The goal of a dynamic MST algorithm is to update efficiently the minimum spanning…
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…
We present a distributed randomized algorithm finding Minimum Spanning Tree (MST) of a given graph in O(1) rounds, with high probability, in the Congested Clique model. The input graph in the Congested Clique model is a graph of n nodes,…
Finding spanning trees under various constraints is a classic problem with applications in many fields. Recently, a novel notion of "dense" ("sparse") tree, and in particular spanning tree (DST and SST respectively), is introduced as the…
For a set of red and blue points in the plane, a minimum bichromatic spanning tree (MinBST) is a shortest spanning tree of the points such that every edge has a red and a blue endpoint. A MinBST can be computed in $O(n\log n)$ time where…
Robust optimization is one of the fundamental approaches to deal with uncertainty in combinatorial optimization. This paper considers the robust spanning tree problem with interval data, which arises in a variety of telecommunication…
Along with the development of manufacture and services, the problem of distribution network optimization has been growing in importance, thus receiving much attention from the research community. One of the most recently introduced network…
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 consider the minimum spanning tree problem with predictions, using the weight-arrival model, i.e., the graph is given, together with predictions for the weights of all edges. Then the actual weights arrive one at a time and an…
We study the problem of privately releasing an approximate minimum spanning tree (MST). Given a graph $G = (V, E, \vec{W})$ where $V$ is a set of $n$ vertices, $E$ is a set of $m$ undirected edges, and $ \vec{W} \in \mathbb{R}^{|E|} $ is an…
In this thesis, we design algorithms for several NP-hard problems in both worst and beyond worst case settings. In the first part of the thesis, we apply the traditional worst case methodology and design approximation algorithms for the Hub…
Minimum Spanning Trees are a well-studied subset of graph problems. While classical algorithms have existed to solve these problems for decades, new variations and application areas are constantly being discovered. When dealing with large…
We consider two natural variants of the problem of minimum spanning tree (MST) of a graph in the parallel setting: MST verification (verifying if a given tree is an MST) and the sensitivity analysis of an MST (finding the lowest cost…