Wireless information networks
Computers and Operations Research
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Power consumption in packet radio networks
Theoretical Computer Science
Fault-tolerant broadcasting in radio networks
Journal of Algorithms
On the Complexity of Computing Minimum Energy Consumption Broadcast Subgraphs
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
IPDPS '03 Proceedings of the 17th International Symposium on Parallel and Distributed Processing
On Minimum-Energy Broadcasting in All-Wireless Networks
LCN '01 Proceedings of the 26th Annual IEEE Conference on Local Computer Networks
On the power assignment problem in radio networks
Mobile Networks and Applications - Discrete algorithms and methods for mobile computing and communications
Minimum-Energy Broadcast and disk cover in grid wireless networks
Theoretical Computer Science
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
The “real” approximation factor of the MST heuristic for the minimum energy broadcasting
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
3-Dimensional minimum energy broadcasting problem
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
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The Minimum Energy Broadcast problem consists in finding the minimum-energy range assignment for a given set S of n stations of an ad hoc wireless network that allows a source station to perform broadcast operations over S We prove a nearly tight asymptotical bound on the optimal cost for the Minimum Energy Broadcast problem on square grids. We emphasize that finding tight bounds for this problem restriction is far to be easy: it involves the Gauss's Circle problem and the Apollonian Circle Packing. We also derive near-tight bounds for the Bounded-Hop version of this problem. Our results imply that the best-known heuristic, the MST-based one, for the Minimum Energy Broadcast problem is far to achieve optimal solutions (even) on very regular, well-spread instances: its worst-case approximation ratio is about π and it yields $\Omega(\sqrt{n})$ hops As a by product, we get nearly tight bounds for the Minimum Disk Cover problem and for its restriction in which the allowed disks must have non-constant radius Finally, we emphasize that our upper bounds are obtained via polynomial time constructions