Abstract
We present a new (1+ε)-spanner for sets of n points in ℝd. Our spanner has size O(n/ε d−1) and maximum degree O(log d n). The main advantage of our spanner is that it can be maintained efficiently as the points move: Assuming that the trajectories of the points can be described by bounded-degree polynomials, the number of topological changes to the spanner is O(n 2/ε d−1), and using a supporting data structure of size O(nlog d n), we can handle events in time O(log d+1 n). Moreover, the spanner can be updated in time O(log n) if the flight plan of a point changes. This is the first kinetic spanner for points in ℝd whose performance does not depend on the spread of the point set.
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M.A. was supported by MADALGO Center for Massive Data Algorithmics, a Center of the Danish National Research Foundation.
M.dB. was supported by the Netherlands’ Organisation for Scientific Research (NWO) under project no 639.023.301.
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Abam, M.A., de Berg, M. Kinetic Spanners in ℝd . Discrete Comput Geom 45, 723–736 (2011). https://doi.org/10.1007/s00454-011-9343-y
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DOI: https://doi.org/10.1007/s00454-011-9343-y