Choi et al. (2011) introduced a minimum spanning tree (MST)-based method called CLGrouping, for constructing tree-structured probabilistic graphical models, a statistical framework that is commonly used for inferring phylogenetic trees. While CLGrouping works correctly if there is a unique MST, we observe an indeterminacy in the method in the case that there are multiple MSTs. In this work we r...

Minimum Spanning Trees (MSTs) are ubiquitous in optimization problems in networks. Even though fast algorithms exist to solve the MST problem, real world applications are usually subject to constraints that do not let us apply such methods directly. In these cases we confront a version of the MST called the “Weighted Spanning Tree” (WST) in which we look for a spanning tree in a graph that sati...

We give a tight analysis of the MST heuristic recently introduced by G.-H. Lin and G. Xue for approximating the Steiner tree with minimum number of Steiner points and bounded edge-lengths. The approximation factor of the heuristic is shown to be one less than the MST number of the underlying space, de ned as the maximum possible degree of a minimum-degree MST spanning points from the space. In ...

* to be exact, times the weight of a minimum spanning tree (MST). In particular, we present an improved analysis of Chan’s degree-4 MST algorithm [4]. Previous results. Arora [1] and Mitchell [9] presented PTASs for TSP in Euclidean metric, for fixed dimensions. Unfortunately, neither algorithm extends to find degree-3 or degree-4 trees. Recently, Arora and Chang [3] have devised a quasi-polyno...

Metaheuristics, such as evolutionary algorithms or simulated annealing, are widely applicable heuristic optimization strategies that have shown encouraging results for a large number of difficult optimization problems. To show high performance, metaheuristics need to be adapted to the properties of the problem at hand. This paper illustrates how efficient metaheuristics can be developed for com...

In this lecture, we discuss a near-optimal distributed algorithm in the CONGEST model for the problem of computing a minimum spanning tree (MST). We note that, over the years, the problem of computing an MST has turned out to have a central role in distributed algorithms for network optimization problems, significantly more central than its role in the centralized algorithms domain. The upper a...

In this paper we consider a natural probabilistic variation of the classical minimum spanning tree problem (MST), which we call the probabilistic minimum spanning tree problem (PMST). In particular, we consider the case where not all the points are deterministically present, but are present with certain probability. We discuss the applications of the PMST and find a closed-form expression for t...

Given a connected graph G = (V, E) with non-negative edge costs, and a set of " special " nodes S ⊂ V , a subgraph of G is a Steiner tree, if it is a tree that spans (connects) all the (" special ") nodes in S. The Steiner Tree problem is to find a Steiner Tree of minimum weight (cost). Steiner Tree is an important NP-hard problem that is often encountered in practice. Examples include design o...

In the minimum-cost k-hop spanning tree (k-hop MST) problem, we are given a set S of n points in a metric space, a positive small integer k and a root point r ∈ S. We are interested in computing a rooted spanning tree of minimum cost such that the longest root-leaf path in the tree has at most k edges. We present a polynomial-time approximation scheme for the plane. Our algorithm is based on Ar...