Minimum-Energy Broadcast and disk cover in grid wireless networks

Authors:
Tiziana Calamoneri;Andrea E. F. Clementi;Miriam Di Ianni;Massimo Lauria;Angelo Monti;Riccardo Silvestri
Affiliations:
Dipartimento di Informatica, Sapienza Università degli Studi di Roma, Italy;Dipartimento di Matematica, Università degli Studi di Roma Tor Vergata, Italy;Dipartimento di Matematica, Università degli Studi di Roma Tor Vergata, Italy;Dipartimento di Informatica, Sapienza Università degli Studi di Roma, Italy;Dipartimento di Informatica, Sapienza Università degli Studi di Roma, Italy;Dipartimento di Informatica, Sapienza Università degli Studi di Roma, Italy
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

The Minimum-Energy Broadcast problem is to assign a transmission range to every station of an ad hoc wireless networks so that (i) a given source station is allowed to perform broadcast operations and (ii) the overall energy consumption of the range assignment is minimized. We prove a nearly tight asymptotical bound on the optimal cost for the Minimum-Energy Broadcast problem on square grids. 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 @p and it yields @W(n) hops, where n is the number of stations. 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.