Computational geometry: an introduction
Computational geometry: an introduction
Delaunay graphs are almost as good as complete graphs
Discrete & Computational Geometry
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
Power-Aware Localized Routing in Wireless Networks
IEEE Transactions on Parallel and Distributed Systems
Geometric ad-hoc routing: of theory and practice
Proceedings of the twenty-second annual symposium on Principles of distributed computing
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
Geometrically aware communication in random wireless networks
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
On the pitfalls of geographic face routing
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
Graph Theory With Applications
Graph Theory With Applications
On delivery guarantees of face and combined greedy-face routing in ad hoc and sensor networks
Proceedings of the 12th annual international conference on Mobile computing and networking
Fast localized delaunay triangulation
OPODIS'04 Proceedings of the 8th international conference on Principles of Distributed Systems
Localized Delaunay triangulation with application in ad hoc wireless networks
IEEE Transactions on Parallel and Distributed Systems
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A localized Delaunay triangulation owns the following interesting properties for sensor and wireless ad hoc networks: 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 two localized algorithms, fast localized Delaunay triangulation 1 (FLDT1) and fast localized Delaunay triangulation 2 (FLDT2), that build a graph called planar localized Delaunay triangulation, PLDel, known to be a good spanner of the Unit Disk Graph, UDG. Our algorithms improve previous algorithms with similar theoretical bounds in the following aspects: unlike previous work, FLDT1 and FLDT2 build PLDel in a single communication step, maintaining a communication cost of O(n log n), which is within a constant of the optimal. Additionally, we show that FLDT1 is more robust than previous triangulation algorithms, because it does not require the strict UDG connectivity model to work. The small signaling cost of our algorithms allows us to improve routing performance, by efficiently using the PLDel graph instead of sparser graphs, like the Gabriel or the Relative Neighborhood graphs.