Open AccessProceedings Article
Competitive Routing on a Bounded-Degree Plane Spanner
Prosenjit Bose,Rolf Fagerberg,André van Renssen,Sander Verdonschot +3 more
- pp 285-290
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TLDR
It is shown that it is possible to route locally and competitively on two bounded-degree plane 6-spanners, one with maximum degree 12 and the other withmaximum degree 9, which are subgraphs of the empty equilateral triangle Delaunay triangulation.Abstract:
We show that it is possible to route locally and competitively on two bounded-degree plane 6-spanners, one with maximum degree 12 and the other with maximum degree 9. Both spanners are subgraphs of the empty equilateral triangle Delaunay triangulation. First, in a weak routing model where the only information stored at each vertex is its neighbourhood, we show how to nd a path between any two vertices of a 6-spanner of maximum degree 12, such that the path has length at most 95= p 3 times the straight-line distance between the vertices. In a slightly stronger model, where in addition to the neighbourhood of each vertex, we store O(1) additional information, we show how to nd a path that has length at most 15= p 3 times the Euclidean distance both in a 6-spanner of maximum degree 12 and a 6-spanner of maximum degree 9.read more
Citations
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Journal ArticleDOI
There are Plane Spanners of Degree 4 and Moderate Stretch Factor
TL;DR: The complete Euclidean graph always contains a plane spanner of maximum degree 4 and this construction leads to an efficient algorithm for obtaining the spanner from Chew’s L1-Delaunay triangulation.
Book ChapterDOI
Upper and Lower Bounds for Online Routing on Delaunay Triangulations
TL;DR: In this paper, the authors consider a weighted graph G whose vertices are points in the plane and edges are line segments between pairs of points whose weight is the Euclidean distance between its endpoints.
Proceedings ArticleDOI
Improved Routing on the Delaunay Triangulation.
TL;DR: An algorithm for 1-local routing on the Delaunay triangulation is presented, and it is shown that it finds a path between a source vertex s and a target vertex t that is not longer than 3.56|st|, improving the previous bound of 5.9.
Posted Content
There are Plane Spanners of Maximum Degree 4
TL;DR: In this article, it was shown that the complete Euclidean graph always contains a plane spanner of maximum degree at most 4 and make a big step toward closing the question.
Posted Content
Flips and Spanners.
TL;DR: This thesis presents a routing strategy on the half-ϴ6-graph, a variant of the graph with 6 cones, and proves tight ϴ(n log n) bounds on the number of flips required in several settings where the edges have unique labels.
References
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Journal ArticleDOI
A note on two problems in connexion with graphs
TL;DR: A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.
Journal ArticleDOI
Searching in the Plane
TL;DR: It is shown that for some simple search problems, knowing the general direction of the goal is much more informative than knowing the distance to the goal.
Book
Geometric Spanner Networks
Giri Narasimhan,Michiel Smid +1 more
TL;DR: In this paper, the authors present rigorous descriptions of the main algorithms and their analyses for different variations of the Geometric Spanner Network Problem, and present several basic principles and results that are used throughout the book.
Journal ArticleDOI
There are planar graphs almost as good as the complete graph
TL;DR: It is shown that there is a planar graph G on S with the property that for any points A and B of S there exists an A-to-B path along edges of the graph with path length equal to the straight-line distance between A and A.
Book
Wireless Ad Hoc and Sensor Networks
TL;DR: This book deals with several relevant fields related to the evolution of these spontaneous and self-organized networks, tackling critical problems such as the design of unicast/multicast routing protocols, the support of the quality of service, the security mechanisms for routing and data transmission, the service discovery, the techniques of clustering/self-organization, the mobility of code and the fault-tolerance techniques.