Related papers: Special Cases of the Minimum Spanning Tree Problem…
We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a connected graph. It is motivated by a particular problem in epidemiology, and may be useful in studies of various dynamical processes in…
We study the problem of low-stretch spanning trees in graphs of bounded width: bandwidth, cutwidth, and treewidth. We show that any simple connected graph $G$ with a linear arrangement of bandwidth $b$ can be embedded into a distribution…
We present an implementation and an experimental evaluation of an algorithm that, given a connected graph G (represented by adjacency lists), estimates in sublinear time, with a relative error, the Minimum Spanning Tree Weight of G; the…
The eternal vertex cover problem is a dynamic variant of the classical vertex cover problem. It is NP-hard to compute the eternal vertex cover number of graphs and known algorithmic results for the problem are very few. This paper presents…
We investigate the Minimum Eccentricity Shortest Path problem in some structured graph classes. It asks for a given graph to find a shortest path with minimum eccentricity. Although it is NP-hard in general graphs, we demonstrate that a…
The degree-d spanning tree problem asks for a minimum-weight spanning tree in which the degree of each vertex is at most d. When d=2 the problem is TSP, and in this case, the well-known Christofides algorithm provides a 1.5-approximation…
In this paper, we consider different constrained partition problems for weighted trees and cactus graphs. We focus on the (l,u)-partition problem, which is the problem of partitioning a weighted graph into connected clusters such that each…
Given a graph $G=(V,E)$ with non-negative real edge lengths and an integer parameter $k$, the Min-Max k-Tree Cover problem seeks to find a set of at most $k$ subtrees of $G$, such that the union of the trees is the vertex set $V$. The…
A complete understanding of real networks requires us to understand the consequences of the uneven interaction strengths between a system's components. Here we use the minimum spanning tree (MST) to explore the effect of weight assignment…
Random spanning trees of a graph $G$ are governed by a corresponding probability mass distribution (or "law"), $\mu$, defined on the set of all spanning trees of $G$. This paper addresses the problem of choosing $\mu$ in order to utilize…
We propose a new algorithm for the solution of the robust multiple-load topology optimization problem. The algorithm can be applied to any type of problem, e.g., truss topology, variable thickness sheet or free material optimization. We…
Previous studies has shown that for a weighted undirected graph having $n$ vertices and $m$ edges, a minimal weight spanning tree can be found with $O^*(\sqrt{mn})$ calls to the weight oracle. The present note shows that a given spanning…
For a given graph $G$, a maximum internal spanning tree of $G$ is a spanning tree of $G$ with maximum number of internal vertices. The Maximum Internal Spanning Tree (MIST) problem is to find a maximum internal spanning tree of the given…
We consider the Shortest Odd Path problem, where given an undirected graph $G$, a weight function on its edges, and two vertices $s$ and $t$ in $G$, the aim is to find an $(s,t)$-path with odd length and, among all such paths, of minimum…
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…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
The run time complexity of state-of-the-art inference algorithms in graph-based dependency parsing is super-linear in the number of input words (n). Recently, pruning algorithms for these models have shown to cut a large portion of the…
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
Given an edge-weighted graph $G=(V,E)$ and a set $E_0\subset E$, the incremental network design problem with minimum spanning trees asks for a sequence of edges $e'_1,\ldots,e'_T\in E\setminus E_0$ minimizing $\sum_{t=1}^Tw(X_t)$ where…
The problem of finding the maximum-weight, planar subgraph of a finite, simple graph with nonnegative real edge weights is well known in industrial and electrical engineering, systems biology, sociology and finance. As the problem is known…