Algorithms for dynamic closest pair and n-body potential fields
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Approximate minimum enclosing balls in high dimensions using core-sets
Journal of Experimental Algorithmics (JEA)
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
On coresets for k-means and k-median clustering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
On hierarchical routing in doubling metrics
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Fast Construction of Nets in Low-Dimensional Metrics and Their Applications
SIAM Journal on Computing
DCOSS '08 Proceedings of the 4th IEEE international conference on Distributed Computing in Sensor Systems
Low-energy fault-tolerant bounded-hop broadcast in wireless networks
IEEE/ACM Transactions on Networking (TON)
Minimum-energy broadcast with few senders
DCOSS'07 Proceedings of the 3rd IEEE international conference on Distributed computing in sensor systems
The min-power multicast problems in wireless ad hoc networks: a parameterized view
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Parameterized complexity of Min-power multicast problems in wireless ad hoc networks
Theoretical Computer Science
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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 O(1/Ɛ)4k) we are able to (1+Ɛ)-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.