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ACM Transactions on Mathematical Software (TOMS)
Approximation algorithms for convex hulls
Communications of the ACM
Distributed Qualitative Localization for Wireless Sensor Networks
ADHOC-NOW '08 Proceedings of the 7th international conference on Ad-hoc, Mobile and Wireless Networks
A minimum energy path topology control algorithm for wireless multihop networks
Proceedings of the 2009 International Conference on Wireless Communications and Mobile Computing: Connecting the World Wirelessly
On channel-discontinuity-constraint routing in wireless networks
INFOCOM'10 Proceedings of the 29th conference on Information communications
Graphics Interaction: A procedural method for irregular tree models
Computers and Graphics
On channel-discontinuity-constraint routing in wireless networks
Ad Hoc Networks
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The problem of finding a minimum spanning tree connecting n points in a k-dimensional space is discussed under three common distance metrics -- Euclidean, rectilinear, and $L_\infty$. By employing a subroutine that solves the post office problem, we show that, for fixed k $\geq$ 3, such a minimum spanning tree can be found in time O($n^{2-a(k)} {(log n)}^{1-a(k)}$), where a(k) = $2^{-(k+1)}$. The bound can be improved to O(${(n log n)}^{1.8}$) for points in the 3-dimensional Euclidean space. We also obtain o($n^2$) algorithms for finding a farthest pair in a set of n points and for other related problems.