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The Minimum Spanning Tree Problem with Conflicts consists in finding the minimum conflict-free spanning tree of a graph, i.e., the spanning tree of minimum cost, including no pairs of edges that are in conflict. In this paper, we solve this…

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 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…

Deep Neural Networks require large amounts of labeled data for their training. Collecting this data at scale inevitably causes label noise.Hence,the need to develop learning algorithms that are robust to label noise. In recent years, k…

K-nearest neighbor (kNN) search has wide applications in many areas, including data mining, machine learning, statistics and many applied domains. Inspired by the success of ensemble methods and the flexibility of tree-based methodology, we…

The Minimum Branch Vertices Spanning Tree problem aims to find a spanning tree $T$ in a given graph $G$ with the fewest branch vertices, defined as vertices with a degree three or more in $T$. This problem, known to be NP-hard, has…

In this paper, we introduce a new problem called Tree-Residue Vertex-Breaking (TRVB): given a multigraph $G$ some of whose vertices are marked "breakable," is it possible to convert $G$ into a tree via a sequence of "vertex-breaking"…

Let $G$ be a connected graph and $T$ a spanning tree of $G$. Let $\rho(G)$ denote the adjacency spectral radius of $G$. The $k$-excess of a vertex $v$ in $T$ is defined as $\max\{0,d_T(v)-k\}$. The total $k$-excess $\mbox{te}(T,k)$ is…

With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The…

The Maximum (Minimum) Leaf Spanning Tree problem asks for a spanning tree with the largest (smallest) number of leaves. As spanning trees are often computed using graph search algorithms, it is natural to restrict this problem to the set of…

We study a maximization problem for geometric network design. Given a set of $n$ compact neighborhoods in $\mathbb{R}^d$, select a point in each neighborhood, so that the longest spanning tree on these points (as vertices) has maximum…

We consider the multi-broadcast problem in arbitrary connected radio networks consisting of $n$ nodes. There are $k$ designated source nodes for some fixed $k \in \{1,\ldots,n\}$, and each source node has a distinct piece of information…

Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…

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…

We address here spanning tree problems on a graph with binary edge weights. For a general weighted graph the minimum spanning tree is solved in super-linear running time, even when the edges of the graph are pre-sorted. A related problem,…

K-Nearest Neighbors (KNN) search is a fundamental algorithm in artificial intelligence software with applications in robotics, and autonomous vehicles. These wide-ranging applications utilize KNN either directly for simple classification or…

We consider the $k$-prize-collecting Steiner tree problem. An instance is composed of an integer $k$ and a graph $G$ with costs on edges and penalties on vertices. The objective is to find a tree spanning at least $k$ vertices which…

Partitioning trees are efficient data structures for $k$-nearest neighbor search. Machine learning libraries commonly use a special type of partitioning trees called $k$d-trees to perform $k$-nn search. Unfortunately, $k$d-trees can be…

Given a set V of n elements on m attributes, we want to find a partition of V on the minimum number of clusters such that the associated R-squared ratio is at least a given threshold. We denote this problem as Goal Clustering (GC). This…

In the spanning tree congestion problem, given a connected graph $G$, the objective is to compute a spanning tree $T$ in $G$ that minimizes its maximum edge congestion, where the congestion of an edge $e$ of $T$ is the number of edges in…