Related papers: Stochastic Minimum Spanning Trees with a Single Sa…
This paper introduces the notion of distributed verification without preprocessing. It focuses on the Minimum-weight Spanning Tree (MST) verification problem and establishes tight upper and lower bounds for the time and message complexities…
In the length-constrained minimum spanning tree (MST) problem, we are given an $n$-node edge-weighted graph $G$ and a length constraint $h \geq 1$. Our goal is to find a spanning tree of $G$ whose diameter is at most $h$ with minimum…
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…
We study the relation between the minimal spanning tree (MST) on many random points and the "near-minimal" tree which is optimal subject to the constraint that a proportion $\delta$ of its edges must be different from those of the MST.…
The seeded Watershed algorithm / minimax semi-supervised learning on a graph computes a minimum spanning forest which connects every pixel / unlabeled node to a seed / labeled node. We propose instead to consider all possible spanning…
Distribution grids refer to the part of the power grid that delivers electricity from substations to the loads. Structurally a distribution grid is operated in one of several radial/tree-like topologies that are derived from an original…
We study the electrical distribution network reconfiguration problem, defined as follows. We are given an undirected graph with a root vertex, demand at each non-root vertex, and resistance on each edge. Then, we want to find a spanning…
In this paper, we aim to design sparse D-optimal (determinantoptimal) pose-graph SLAM problems through the synthesis of sparse graphs with the maximum weighted number of spanning trees. Characterizing graphs with the maximum number of…
We study budget constrained network upgradeable problems. We are given an undirected edge weighted graph $G=(V,E)$ where the weight an edge $e \in E$ can be upgraded for a cost $c(e)$. Given a budget $B$ for improvement, the goal is to find…
Spanning trees are an important primitive in many data analysis tasks, when a data set needs to be summarized in terms of its "skeleton", or when a tree-shaped graph over all observations is required for downstream processing. Popular…
We consider the minimum spanning tree (MST) problem under the restriction that for every vertex v, the edges of the tree that are adjacent to v satisfy a given family of constraints. A famous example thereof is the classical…
We address the problem of efficiently gathering correlated data from a wired or a wireless sensor network, with the aim of designing algorithms with provable optimality guarantees, and understanding how close we can get to the known…
We present a uniform self-stabilizing algorithm, which solves the problem of distributively finding a minimum diameter spanning tree of an arbitrary positively real-weighted graph. Our algorithm consists in two stages of stabilizing…
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…
This paper makes two main contributions: The first is the construction of a near-minimum spanning tree with constant average distortion. The second is a general equivalence theorem relating two refined notions of distortion: scaling…
This paper investigates the problem of regression model generation. A model is a superposition of primitive functions. The model structure is described by a weighted colored graph. Each graph vertex corresponds to some primitive function.…
Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a…
We study the minimal spanning arborescence which is the directed analogue of the minimal spanning tree, with a particular focus on its infinite volume limit and its geometric properties. We prove that in a certain large class of transient…
Given an undirected graph $G = (V, E)$ and a weight function $w:E \to \mathbb{R}$, the \textsc{Minimum Dominating Tree} problem asks to find a minimum weight sub-tree of $G$, $T = (U, F)$, such that every $v \in V \setminus U$ is adjacent…
We study the minimum spanning arborescence problem on the complete digraph $\vec{K}_n$ where an edge $e$ has a weight $W_e$ and a cost $C_e$, each of which is an independent uniform random variable $U^\alpha$ where $\alpha\leq 1$ and $U$ is…