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Summary: Euclidean Spanners: Short, Thin, and Lanky
Sunil Arya Gautam Dasy David M. Mountz Je rey S. Salowex Michiel Smid
Abstract
Euclidean spanners are important data structures
in geometric algorithm design, because they pro-
vide a means of approximating the complete Eu-
clidean graph with only O(n) edges, so that the
shortest path length between each pair of points is
not more than a constant factor longer than the
Euclidean distance between the points. In many
applications of spanners, it is important that the
spanner possess a number of additional properties:
low total edge weight, bounded degree, and low
diameter. Existing research on spanners has con-
sidered one property or the other. We show that it
is possible to build spanners in optimal O(nlogn)
time and O(n) space that achieve optimal or near
optimal tradeo s between all combinations of these
Max-Planck-Institut fur Informatik, D-66123 Saarbruc-
ken, Germany. Email: farya,michielg@mpi-sb.mpg.de.
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