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Related papers: Minimum Sum Dipolar Spanning Tree in R^3

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Let $G$ be a (possibly disconnected) planar subdivision and let $D$ be a probability measure over $\R^2$. The current paper shows how to preprocess $(G,D)$ into an O(n) size data structure that can answer planar point location queries over…

Computational Geometry · Computer Science 2010-01-18 Prosenjit Bose , Luc Devroye , Karim Douieb , Vida Dujmovic , James King , Pat Morin

In the $k$-edge-connected spanning subgraph ($k$ECSS) problem, our goal is to compute a minimum-cost sub-network that is resilient against up to $k$ link failures: Given an $n$-node $m$-edge graph with a cost function on the edges, our goal…

There are several known data structures that answer distance queries between two arbitrary vertices in a planar graph. The tradeoff is among preprocessing time, storage space and query time. In this paper we present three data structures…

Data Structures and Algorithms · Computer Science 2011-02-23 Yahav Nussbaum

Bounded-angle (minimum) spanning trees were first introduced in the context of wireless networks with directional antennas. They are reminiscent of bounded-degree spanning trees, which have received significant attention. Let $P =…

Computational Geometry · Computer Science 2020-10-23 Stav Ashur , Matthew J. Katz

We present a new algorithm for generating a uniformly random spanning tree in an undirected graph. Our algorithm samples such a tree in expected $\tilde{O}(m^{4/3})$ time. This improves over the best previously known bound of…

Data Structures and Algorithms · Computer Science 2017-03-16 Aleksander Madry , Damian Straszak , Jakub Tarnawski

A graph is rectilinear planar if it admits a planar orthogonal drawing without bends. While testing rectilinear planarity is NP-hard in general (Garg and Tamassia, 2001), it is a long-standing open problem to establish a tight upper bound…

Data Structures and Algorithms · Computer Science 2023-06-23 Walter Didimo , Michael Kaufmann , Giuseppe Liotta , Giacomo Ortali

The minimum-weight $2$-edge-connected spanning subgraph (2-ECSS) problem is a natural generalization of the well-studied minimum-weight spanning tree (MST) problem, and it has received considerable attention in the area of network design.…

Data Structures and Algorithms · Computer Science 2019-06-04 Michal Dory , Mohsen Ghaffari

A novel approach for non-intrusive uncertainty propagation is proposed. Our approach overcomes the limitation of many traditional methods, such as generalised polynomial chaos methods, which may lack sufficient accuracy when the quantity of…

Numerical Analysis · Mathematics 2018-03-20 Yous van Halder , Benjamin Sanderse , Barry Koren

The cost-distance Steiner tree problem seeks a Steiner tree that minimizes the total congestion cost plus the weighted sum of source-sink delays. This problem arises as a subroutine in timing-constrained global routing with a linear delay…

Data Structures and Algorithms · Computer Science 2025-03-07 Stephan Held , Edgar Perner

The problem of computing a connected network with minimum interference is a fundamental problem in wireless sensor networks. Several models of interference have been studied in the literature. The most common model is the receiver-centric,…

Computational Geometry · Computer Science 2020-04-21 A. Karim Abu-Affash , Paz Carmi , Matthew J. Katz

In this paper the minimum spanning tree problem with uncertain edge costs is discussed. In order to model the uncertainty a discrete scenario set is specified and a robust framework is adopted to choose a solution. The min-max, min-max…

Computational Complexity · Computer Science 2010-04-19 Adam Kasperski , Pawel Zielinski

The Euclidean Steiner Minimal Tree problem takes as input a set $\mathcal P$ of points in the Euclidean plane and finds the minimum length network interconnecting all the points of $\mathcal P$. In this paper, in continuation to the works…

Computational Geometry · Computer Science 2023-07-04 Anubhav Dhar , Soumita Hait , Sudeshna Kolay

This paper studies Minimum Spanning Trees under incomplete information for its vertices. We assume that no information is available on the precise placement of vertices so that it is only known that vertices belong to some neighborhoods…

Optimization and Control · Mathematics 2016-11-10 Víctor Blanco , Elena Fernández , Justo Puerto

We consider the problem of finding the smallest graph that contains two input trees each with at most $n$ vertices preserving their distances. In other words, we look for an isometric-universal graph with the minimum number of vertices for…

Data Structures and Algorithms · Computer Science 2025-06-17 Edgar Baucher , François Dross , Cyril Gavoille

Let $P \subset \mathbb{R}^2$ be a planar $n$-point set such that each point $p \in P$ has an associated radius $r_p > 0$. The transmission graph $G$ for $P$ is the directed graph with vertex set $P$ such that for any $p, q \in P$, there is…

Computational Geometry · Computer Science 2020-10-05 Haim Kaplan , Wolfgang Mulzer , Liam Roditty , Paul Seiferth

In the \emph{$k$-Diameter-Optimally Augmenting Tree Problem} we are given a tree $T$ of $n$ vertices as input. The tree is embedded in an unknown \emph{metric} space and we have unlimited access to an oracle that, given two distinct…

Data Structures and Algorithms · Computer Science 2023-05-30 Davide Bilò , Luciano Gualà , Stefano Leucci , Luca Pepè Sciarria

We present an algorithm that, with high probability, generates a random spanning tree from an edge-weighted undirected graph in $\tilde{O}(n^{4/3}m^{1/2}+n^{2})$ time (The $\tilde{O}(\cdot)$ notation hides $\operatorname{polylog}(n)$…

Data Structures and Algorithms · Computer Science 2017-06-22 David Durfee , Rasmus Kyng , John Peebles , Anup B. Rao , Sushant Sachdeva

We prove that the spanning trees of any outerplanar triangulation $G$ can be listed so that any two consecutive spanning trees differ in an exchange of two edges that share an end vertex. For outerplanar graphs $G$ with faces of arbitrary…

Discrete Mathematics · Computer Science 2024-12-23 Nastaran Behrooznia , Torsten Mütze

The min-distance between two nodes $u, v$ is defined as the minimum of the distance from $v$ to $u$ or from $u$ to $v$, and is a natural distance metric in DAGs. As with the standard distance problems, the Strong Exponential Time Hypothesis…

Data Structures and Algorithms · Computer Science 2022-10-05 Mina Dalirrooyfard , Jenny Kaufmann

We propose faster algorithms for the following three optimization problems on $n$ collinear points, i.e., points in dimension one. The first two problems are known to be NP-hard in higher dimensions. 1- Maximizing total area of disjoint…

Computational Geometry · Computer Science 2018-07-27 Ahmad Biniaz , Prosenjit Bose , Paz Carmi , Anil Maheshwari , J. Ian Munro , Michiel Smid