There is a planar graph almost as good as the complete graph
SCG '86 Proceedings of the second annual symposium on Computational geometry
GPSR: greedy perimeter stateless routing for wireless networks
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
On constructing minimum spanning trees in k-dimensional spaces and related problems
On constructing minimum spanning trees in k-dimensional spaces and related problems
SPT-based topology algorithm for constructing power efficient wireless ad hoc networks
Proceedings of the 13th international World Wide Web conference on Alternate track papers & posters
A cone-based distributed topology-control algorithm for wireless multi-hop networks
IEEE/ACM Transactions on Networking (TON)
Localized topology control algorithms for heterogeneous wireless networks
IEEE/ACM Transactions on Networking (TON)
S-XTC: A Signal-Strength Based Topology Control Algorithm for Sensor Networks
ISADS '07 Proceedings of the Eighth International Symposium on Autonomous Decentralized Systems
CLTC: A Cluster-Based Topology Control Framework for Ad Hoc Networks
IEEE Transactions on Mobile Computing
Minimum energy mobile wireless networks
IEEE Journal on Selected Areas in Communications
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Devices in wireless multihop networks should communicate with each other along minimum energy-consuming paths for energy-saving. To this end, any energy-aware topology control scheme should not destroy these paths. The Localized Dijkstra Topology Control (LDTC) algorithm discussed in this paper aims at constructing a network topology to preserve all the minimum energy paths by using only local information subject to network connectivity. It also takes link quality requirements to assign transmission power. Furthermore, LDTC is proven analytically that it can maintain bidirectional wireless links to facilitate handshake mechanisms. Moreover, within the Euclidean graph, no two links intersect in the derived topology, which can mitigate interference. Simulation results indicate that LDTC generates a simple topology with small node degree and short transmission radius. When cooperating with different routing strategies, it performs well in energy and hop count spanners, and can be easily implemented in wireless multihop networks.