Computational geometry: an introduction
Computational geometry: an introduction
There is a planar graph almost as good as the complete graph
SCG '86 Proceedings of the second annual symposium on Computational geometry
There are planar graphs almost as good as the complete graph
Journal of Computer and System Sciences
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
The Delauney Triangulation Closely Approximates the Complete Euclidean Graph
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Graph Theory With Applications
Graph Theory With Applications
Delaunay graphs are almost as good as complete graphs
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Geometric Spanners for Wireless Ad Hoc Networks
IEEE Transactions on Parallel and Distributed Systems
Localized construction of bounded degree and planar spanner for wireless ad hoc networks
DIALM-POMC '03 Proceedings of the 2003 joint workshop on Foundations of mobile computing
Spatiotemporal multicast in sensor networks
Proceedings of the 1st international conference on Embedded networked sensor systems
Localized algorithms for energy efficient topology in wireless ad hoc networks
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
Reducing interference in ad hoc networks through topology control
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
A unified energy-efficient topology for unicast and broadcast
Proceedings of the 11th annual international conference on Mobile computing and networking
Localized construction of bounded degree and planar spanner for wireless ad hoc networks
Mobile Networks and Applications
Localized algorithms for energy efficient topology in wireless ad hoc networks
Mobile Networks and Applications
Energy-efficient topology control for three-dimensional sensor networks
International Journal of Sensor Networks
Constrained Delaunay triangulation for ad hoc networks
Journal of Computer Systems, Networks, and Communications
A Data Dissemination Algorithm Based on Geographical Quorum System in Wireless Sensor Networks
CNSR '09 Proceedings of the 2009 Seventh Annual Communication Networks and Services Research Conference
Sharp thresholds for relative neighborhood graphs in wireless ad hoc networks
IEEE Transactions on Wireless Communications
Efficient construction of low weight bounded degree planar spanner
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Topology control and geographic routing in realistic wireless networks
ADHOC-NOW'07 Proceedings of the 6th international conference on Ad-hoc, mobile and wireless networks
EEGFGR: an energy-efficient greedy-face geographic routing for wireless sensor networks
NPC'07 Proceedings of the 2007 IFIP international conference on Network and parallel computing
Autonomous sub-image matching for two-dimensional electrophoresis gels using MaxRST algorithm
Image and Vision Computing
WASA'06 Proceedings of the First international conference on Wireless Algorithms, Systems, and Applications
Dynamic delaunay triangulation for wireless ad hoc network
APPT'05 Proceedings of the 6th international conference on Advanced Parallel Processing Technologies
Randomized AB-Face-AB routing algorithms in mobile ad hoc networks
ADHOC-NOW'05 Proceedings of the 4th international conference on Ad-Hoc, Mobile, and Wireless Networks
On the distribution of typical shortest-path lengths in connected random geometric graphs
Queueing Systems: Theory and Applications
Fault-tolerant spanners for ad hoc networks
International Journal of Network Management
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The spanning ratio of a graph defined on n points in the Euclidean plane is the maximal ratio over all pairs of data points (u, v), of the minimum graph distance between u and v, over the Euclidean distance between u and v. A connected graph is said to be a k-spanner if the spanning ratio does not exceed k. For example, for any k, there exists a point set whose minimum spanning tree is not a k-spanner. At the other end of the spectrum, a Delaunay triangulation is guaranteed to be a 2.42- spanner[11]. For proximity graphs inbetween these two extremes, such as Gabriel graphs[8], relative neighborhood graphs[16] and 脽-skeletons[12] with 脽 驴 [0, 2] some interesting questions arise. We show that the spanning ratio for Gabriel graphs (which are 脽-skeletons with 脽 = 1) is 驴(驴n) in the worst case. For all 脽-skeletons with 脽 驴 [0, 1], we prove that the spanning ratio is at most O(n驴) where 驴 = (1 - log2(1 +驴1 - 脽2))/2. For all 脽-skeletons with 脽 驴 [1, 2), we prove that there exist point sets whose spanning ratio is at least (1/2- o(1) 驴n. For relative neighborhood graphs[16] (skeletons with 脽 = 2), we show that there exist point sets where the spanning ratio is 驴(n). For points drawn independently from the uniform distribution on the unit square, we show that the spanning ratio of the (random) Gabriel graph and all 脽-skeletons with 脽 驴 [1, 2] tends to 驴 in probability as 驴log n/ log log n.