Computational geometry: an introduction
Computational geometry: an introduction
On the randomized construction of the Delaunay tree
Theoretical Computer Science
Routing with guaranteed delivery in ad hoc wireless networks
DIALM '99 Proceedings of the 3rd international workshop on Discrete algorithms and methods for mobile computing and communications
GPSR: greedy perimeter stateless routing for wireless networks
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
Geometric spanner for routing in mobile networks
MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
Asymptotically optimal geometric mobile ad-hoc routing
DIALM '02 Proceedings of the 6th international workshop on Discrete algorithms and methods for mobile computing and communications
Online Routing in Triangulations
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Geometric Spanners for Wireless Ad Hoc Networks
ICDCS '02 Proceedings of the 22 nd International Conference on Distributed Computing Systems (ICDCS'02)
Application-Layer Multicasting with Delaunay Triangulation Overlays
Application-Layer Multicasting with Delaunay Triangulation Overlays
Partial Delaunay Triangulation and Degree Limited Localized Bluetooth Scatternet Formation
IEEE Transactions on Parallel and Distributed Systems
Position-based routing in ad hoc networks
IEEE Communications Magazine
Single-step creation of localized Delaunay triangulations
Wireless Networks
Communication-efficient construction of the plane localized delaunay graph
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Theoretical Computer Science
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A localized Delaunay triangulation owns the following interesting properties in a wireless ad hoc setting: it can be built with localized information, the communication cost imposed by control information is limited and it supports geographical routing algorithms that offer guaranteed convergence. This paper presents a localized algorithm that builds a graph called planar localized Delaunay triangulation, PLDel, known to be a good spanner of the unit disk graph, UDG. Unlike previous work, our algorithm builds PLDel in a single communication step, maintaining a communication cost of O(n log n), which is within a constant of the optimum. This represents a significant practical improvement over previous algorithms with similar theoretical bounds. Furthermore, the small cost of our algorithm makes feasible to use PLDel in real systems, instead of the Gabriel or the Relative Neighborhood graphs, which are not good spanners of UDG.