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Conference Paper

Bounded-hop Energy-efficient Broadcast in Low-dimensional Metrics Via Coresets

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons44464

Funke,  Stefan
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44893

Laue,  Sören
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Funke, S., & Laue, S. (2007). Bounded-hop Energy-efficient Broadcast in Low-dimensional Metrics Via Coresets. In W. Thomas, & P. Weil (Eds.), STACS 2007 (pp. 272-283). Berlin: Springer. doi:10.1007/978-3-540-70918-3_24.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-1E79-2
Abstract
We consider the problem of assigning powers to nodes of a wireless network in the plane such that a message from a source node s reaches all other nodes within a bounded number k of transmissions and the total amount of assigned energy is minimized. By showing the existence of a coreset of size we are able to (1 + ε)-approximate the bounded-hop broadcast problem in time linear in n which is a drastic improvement upon the previously best known algorithm. While actual network deployments often are in a planar setting, the experienced metric for several reasons is typically not exactly of the Euclidean type, but in some sense ’close’. Our algorithm (and others) also work for non-Euclidean metrics provided they exhibit a certain similarity to the Euclidean metric which is known in the literature as bounded doubling dimension. We give a novel characterization of such metrics also pointing out other applications such as space-efficient routing schemes. This work was supported by the Max Planck Center for Visual Computing and Communication (MPC-VCC) funded by the German Federal Ministry of Education and Research (FKZ 01IMC01).