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Approximate Strong Edge-Colouring of Unit Disk Graphs
2020We show that the strong chromatic index of unit disk graphs is efficiently 6-approximable. This improves on 8-approximability as shown by Barrett, Istrate, Kumar, Marathe, Thite, and Thulasidasan [1]. We also show that strong edge-6-colourability is NP-complete for the class of unit disk graphs.
Grelier, Nicolas +3 more
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Weighted CDS in Unit Disk Graph
2012It was open for many years whether MinW-CDS in unit disk graphs has a polynomial-time constant-approximation or not. Ambuhl et al. [2] discovered the first one. Their solution consists of two stages. At the first stage, they construct a dominating set which is a 72-approximation for the minimum-weight dominating set problem in unit disk graphs as ...
Ding-Zhu Du, Peng-Jun Wan
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Secure connected domination and secure total domination in unit disk graphs and rectangle graphs
Theoretical Computer Science, 2023Shou-Jun Xu
exaly
A novel data structure for unit disk graphs
2005Doubly connected edge list are used in computational geometry to represent plane graphs. The authors suggest an extension that covers unit-disk graphs too, and use it in a routing algorithm.
Li, J. +4 more
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Plane Hop Spanners for Unit Disk Graphs
2019The unit disk graph (UDG) is a widely employed model for the study of wireless networks. In this model, wireless nodes are represented by points in the plane and there is an edge between two points if and only if their Euclidean distance is at most one.
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Tree covers of unit disk graphs
We study the tree cover problem of the unit disk graph(UDG) metric, which is the shortest path distance metric induced by UDGs. We show that the UDG of a set of n points in the plane has a tree cover of O(1) trees with distortion O(1) in both weighted and unweighted settings.openaire +1 more source
Minimum connected dominating sets and maximal independent sets in unit disk graphs
Theoretical Computer Science, 2006Weili Wu, Xiaohua Jia
exaly
MAX-CUT and MAX-BISECTION are NP-hard on unit disk graphs
Theoretical Computer Science, 2007Jose Maria Diaz Cort
exaly
Minimum bisection is NP-hard on unit disk graphs
Information and Computation, 2017George B Mertzios
exaly
A simple improved distributed algorithm for minimum CDS in unit disk graphs
ACM Transactions on Sensor Networks, 2006Michael Segal
exaly