Related papers: Clustering with minimum spanning trees: How good c…
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…
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…
This paper proposes an efficient hypergraph partitioning framework based on a novel multi-objective non-convex constrained relaxation model. A modified accelerated proximal gradient algorithm is employed to generate diverse $k$-dimensional…
In recent years there has been a paradigm shift from the study of local task-related activation to the organization and functioning of large-scale functional and structural brain networks. However, a long-standing challenge in this…
The fractal dimension of minimal spanning trees on percolation clusters is estimated for dimensions $d$ up to $d=5$. A robust analysis technique is developed for correlated data, as seen in such trees. This should be a robust method…
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…
The minimum spanning tree (MST), a graph constructed from a distribution of points, draws lines between pairs of points so that all points are linked in a single skeletal structure that contains no loops and has minimal total edge length.…
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…
Algorithms for dynamically maintaining minimum spanning trees (MSTs) have received much attention in both the parallel and sequential settings. While previous work has given optimal algorithms for dense graphs, all existing parallel…
State-of-the-art clustering algorithms use heuristics to partition the feature space and provide little insight into the rationale for cluster membership, limiting their interpretability. In healthcare applications, the latter poses a…
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…
One of the main challenges for hierarchical clustering is how to appropriately identify the representative points in the lower level of the cluster tree, which are going to be utilized as the roots in the higher level of the cluster tree…
Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…
We use the Minimal Spanning Tree to characterize the aggregation level of given sets of points. We test 3 distances based on the histogram of the MST edges to discriminate between the distributions. We calibrate the method by using…
We introduce a cluster evaluation technique called Tree Index. Our Tree Index algorithm aims at describing the structural information of the clustering rather than the quantitative format of cluster-quality indexes (where the representation…
In this article, we study the Euclidean minimum spanning tree problem in an imprecise setup. The problem is known as the \emph{Minimum Spanning Tree Problem with Neighborhoods} in the literature. We study the problem where the neighborhoods…
Standard agglomerative clustering suggests establishing a new reliable linkage at every step. However, in order to provide adaptive, density-consistent and flexible solutions, we study extracting all the reliable linkages at each step,…
We study the distributed minimum spanning tree (MST) problem, a fundamental problem in distributed computing. It is well-known that distributed MST can be solved in $\tilde{O}(D+\sqrt{n})$ rounds in the standard CONGEST model (where $n$ is…
Investigations of mass segregation are of vital interest for the understanding of the formation and dynamical evolution of stellar systems on a wide range of spatial scales. Our method is based on the minimum spanning tree (MST) that serves…
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…