There is a planar graph almost as good as the complete graph
SCG '86 Proceedings of the second annual symposium on Computational geometry
Data networks
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A sparse graph almost as good as the complete graph on points in K dimensions
Discrete & Computational Geometry
New sparseness results on graph spanners
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Wireless information networks
Fast Algorithms for Constructing t-Spanners and Paths with Stretch t
SIAM Journal on Computing
Faster algorithms for some geometric graph problems in higher dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Power consumption in packet radio networks
Theoretical Computer Science
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Channel access scheduling in Ad Hoc networks with unidirectional links
DIALM '01 Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications
Geometric spanner for routing in mobile networks
MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
Power optimization in routing protocols for wireless and mobile networks
Handbook of wireless networks and mobile computing
Mobile ad hoc networking and the IETF
ACM SIGMOBILE Mobile Computing and Communications Review
"Balls into Bins" - A Simple and Tight Analysis
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Hardness Results for the Power Range Assignmet Problem in Packet Radio Networks
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Energy-efficient collision-free medium access control for wireless sensor networks
Proceedings of the 1st international conference on Embedded networked sensor systems
Does topology control reduce interference?
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
Journal of the ACM (JACM)
Algorithmic aspects of topology control problems for ad hoc networks
Mobile Networks and Applications
Energy efficient communication in ad hoc networks from user's and designer's perspective
ACM SIGMOBILE Mobile Computing and Communications Review
Reducing interference in ad hoc networks through topology control
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile computing
Fault-Tolerant Power Assignment and Backbone in Wireless Networks
PERCOMW '06 Proceedings of the 4th annual IEEE international conference on Pervasive Computing and Communications Workshops
Topology control meets SINR: the scheduling complexity of arbitrary topologies
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
Geometric Spanner Networks
Geometric spanners with applications in wireless networks
Computational Geometry: Theory and Applications
Computing a minimum-dilation spanning tree is NP-hard
CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65
Asymptotic critical total power for k-connectivity of wireless networks
IEEE/ACM Transactions on Networking (TON)
On triangulations of a set of points in the plane
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Reliable Key Establishment Scheme Exploiting Unidirectional Links in Wireless Sensor Networks
EUC '08 Proceedings of the 2008 IEEE/IFIP International Conference on Embedded and Ubiquitous Computing - Volume 01
Computing geometric minimum-dilation graphs is NP-hard
GD'06 Proceedings of the 14th international conference on Graph drawing
Localized spanner construction for ad hoc networks with variable transmission range
ACM Transactions on Sensor Networks (TOSN)
Minimum power energy spanners in wireless ad hoc networks
INFOCOM'10 Proceedings of the 29th conference on Information communications
Near-optimal multicriteria spanner constructions in wireless ad hoc networks
IEEE/ACM Transactions on Networking (TON)
Novel algorithms for the network lifetime problem in wireless settings
Wireless Networks
On spanners of geometric graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
The design space of wireless sensor networks
IEEE Wireless Communications
Bounded-Hop Energy-Efficient Liveness of Flocking Swarms
IEEE Transactions on Mobile Computing
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We study the problem of spanner construction in wireless ad-hoc networks through power assignments under two spanner models—distance and energy. In particular, we are interested in asymmetric power assignments so that the induced communication graph holds good distance and energy stretch factors simultaneously. In addition, we consider the following optimization objectives: low total energy consumption, low interference level, low hopdiameter, and high network lifetime. Two node deployment scenarios are studied: random and deterministic. For n random nodes distributed uniformly and independently in a unit square, we present several power assignments with varying construction-time complexities. The results are based on various geometric properties of random points and shortest path tree constructions. Due to the probabilistic nature of this scenario, the probability of our results converges to one as the number of network nodes, n, increases. For the deterministic case, we present two power assignments with nontrivial bounds. These are established in addition to shortcut edges that satisfy desired threshold stretch. To the best of our knowledge, these are the first results for spanner construction in wireless ad-hoc networks with provable bounds for both energy and distance metrics simultaneously. Our power assignments, in addition, try optimizing additional network properties, such as network lifetime, interference, and hop diameter.