Related papers: Finding a Minimum Spanning Tree with a Small Non-T…
Consider~\(n\) nodes~\(\{X_i\}_{1 \leq i \leq n}\) independently distributed in the unit square~\(S,\) each according to a distribution~\(f.\) Nodes~\(X_i\) and~\(X_j\) are joined by an edge if the Euclidean distance~\(d(X_i,X_j)\) is less…
For a metric graph $G=(V,E)$ and $R\subset V$, the internal Steiner minimum tree problem asks for a minimum weight Steiner tree spanning $R$ such that every vertex in $R$ is not a leaf. This note shows a simple polynomial-time…
We give polynomial time logarithmic approximation guarantees for the budget minimization, as well as for the profit maximization versions of minimum spanning tree interdiction. In this problem, the goal is to remove some edges of an…
We present approximation algorithms for the following NP-hard optimization problems related to bottleneck spanning trees in metric spaces. 1. The disjoint bottleneck spanning tree problem: Given $n$ pairs of points in a metric space, find…
In this paper, we introduce the Fixed Topology Minimum-Length Tree with Neighborhood Problem, which aims to embed a rooted tree-shaped graph into a $d$-dimensional metric space while minimizing its total length provided that the nodes must…
We attempt to shed new light on the notion of 'tree-like' metric spaces by focusing on an approach that does not use the four-point condition. Our key question is: Given metric space $M$ on $n$ points, when does a fully labelled…
In the complete graph on n vertices, when each edge has a weight which is an exponential random variable, Frieze proved that the minimum spanning tree has weight tending to zeta(3)=1/1^3+1/2^3+1/3^3+... as n goes to infinity. We consider…
The minimum spanning tree of a graph is a well-studied structure that is the basis of countless graph theoretic and optimization problem. We study the minimum spanning tree (MST) perturbation problem where the goal is to spend a fixed…
We study the NP-hard Minimum Shared Edges (MSE) problem on graphs: decide whether it is possible to route $p$ paths from a start vertex to a target vertex in a given graph while using at most $k$ edges more than once. We show that MSE can…
We study set selection problems where the weights are uncertain. Instead of its exact weight, only an uncertainty interval containing its true weight is available for each element. In some cases, some solutions are universally optimal;…
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.,…
A vertex of degree one in a tree is called an end vertex and a vertex of degree at least three is called a branch vertex. For a graph $G$, let $\sigma_2$ be the minimum degree sum of two nonadjacent vertices in $G$. We consider tree…
In Terminal Monitoring Set (TMS), the input is an undirected graph $G=(V,E)$, together with a collection $T$ of terminal pairs and the goal is to find a subset $S$ of minimum size that hits a shortest path between every pair of terminals.…
Color-constrained subgraph problems are those where we are given an edge-colored (directed or undirected) graph and the task is to find a specific type of subgraph, like a spanning tree, an arborescence, a single-source shortest path tree,…
We study the weighted token swapping problem, in which we are given a graph on $n$ vertices, $n$ weighted tokens, an initial assignment of one token to each vertex, and a final assignment of one token to each vertex. The goal is to find a…
The Angular Constrained Minimum Spanning Tree Problem ($\alpha$-MSTP) is defined in terms of a complete undirected graph $G=(V,E)$ and an angle $\alpha \in (0,2\pi]$. Vertices of $G$ define points in the Euclidean plane while edges, the…
In the longest plane spanning tree problem, we are given a finite planar point set $\mathcal{P}$, and our task is to find a plane (i.e., noncrossing) spanning tree for $\mathcal{P}$ with maximum total Euclidean edge length. Despite more…
We consider the minimum cut problem in undirected, weighted graphs. We give a simple algorithm to find a minimum cut that $2$-respects (cuts two edges of) a spanning tree $T$ of a graph $G$. This procedure can be used in place of the…
This paper considers the \textit{minimum spanning tree (MST)} problem in the Congested Clique model and presents an algorithm that runs in $O(\log \log \log n)$ rounds, with high probability. Prior to this, the fastest MST algorithm in this…
Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios, often requiring intricate algorithmic design and exponential time. Recently, there has been growing interest in end-to-end deep neural…