Proceedings of the twenty-ninth annual symposium on Computational geometry
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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.