Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Power-aware routing in mobile ad hoc networks
MobiCom '98 Proceedings of the 4th annual ACM/IEEE international conference on Mobile computing and networking
Adaptive protocols for information dissemination in wireless sensor networks
MobiCom '99 Proceedings of the 5th annual ACM/IEEE international conference on Mobile computing and networking
Next century challenges: scalable coordination in sensor networks
MobiCom '99 Proceedings of the 5th annual ACM/IEEE international conference on Mobile computing and networking
Next century challenges: mobile networking for “Smart Dust”
MobiCom '99 Proceedings of the 5th annual ACM/IEEE international conference on Mobile computing and networking
Wireless integrated network sensors
Communications of the ACM
GPSR: greedy perimeter stateless routing for wireless networks
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
A Distributed Algorithm for Minimum-Weight Spanning Trees
ACM Transactions on Programming Languages and Systems (TOPLAS)
Static and kinetic geometric spanners with applications
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Geometric spanner for routing in mobile networks
MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
Constructing minimum energy mobile wireless networks
MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
Routing with guaranteed delivery in ad hoc wireless networks
Wireless Networks
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
Energy Efficient Design of Wireless Ad Hoc Networks
NETWORKING '02 Proceedings of the Second International IFIP-TC6 Networking Conference on Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; and Mobile and Wireless Communications
Worst-Case optimal and average-case efficient geometric ad-hoc routing
Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
Energy-Efficient Communication Protocol for Wireless Microsensor Networks
HICSS '00 Proceedings of the 33rd Hawaii International Conference on System Sciences-Volume 8 - Volume 8
Geometric ad-hoc routing: of theory and practice
Proceedings of the twenty-second annual symposium on Principles of distributed computing
IEEE Communications Magazine
On the Longest Edge of Gabriel Graphs in Wireless Ad Hoc Networks
IEEE Transactions on Parallel and Distributed Systems
Grid emulation for managing random sensor networks
Ad Hoc Networks
Minimum-energy broadcast in random-grid ad-hoc networks: approximation and distributed algorithms
Proceedings of the 11th international symposium on Modeling, analysis and simulation of wireless and mobile systems
Sharp thresholds for relative neighborhood graphs in wireless ad hoc networks
IEEE Transactions on Wireless Communications
Single-step creation of localized Delaunay triangulations
Wireless Networks
Tell me where i am so i can meet you sooner: asynchronous rendezvous with location information
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Almost optimal asynchronous rendezvous in infinite multidimensional grids
DISC'10 Proceedings of the 24th international conference on Distributed computing
Synchronous rendezvous for location-aware agents
DISC'11 Proceedings of the 25th international conference on Distributed computing
Managing random sensor networks by means of grid emulation
NETWORKING'06 Proceedings of the 5th international IFIP-TC6 conference on Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; Mobile and Wireless Communications Systems
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Some of the first routing algorithms for position-aware wireless networks used the Delaunay triangulation of the point-locations of the network's nodes as the underlying connectivity graph. Later on these solutions were considered impractical because the Delaunay triangulation may in general contain arbitrarily long edges and because calculating the Delaunay triangulation may require a global view of the network. Many other algorithms were then suggested for geometric routing, often assuming random placement of network nodes for analysis or simulation [27, 5, 28, 15]. But as we show, when the nodes are uniformly placed in the unit disk the Delaunay triangulation does not contain long edges, it is easy to compute locally and it is in many ways optimal for geometric routing and flooding.In particular, we prove that with high probability the maximal length of an edge in Del(P), the Delaunay triangulation of a set P of n nodes uniformly placed in the unit disk, is O(3√3log novern), and that the expected sum of squares of all the edges in Del(P) is O(1). These geometric results imply that for wireless networks, randomly distributed in a unit disk (1) computing the Delaunay triangulation locally is asymptotically easy; (2) simple "face routing" through the Delaunay triangulation optimizes, up to poly-logarithmic factors, the energy load on the nodes, and (3) flooding the network, an operation quite common in sensor nets, is with high probability optimal up to a constant factor. The last property is particularly important for geocasting because the Delaunay triangulation is known to be a spanner.