Kinetic spanners in Rd

We present a new (1 + ε)-spanner for sets of n points in Rd . Our spanner has size O(n/εd−1 ) and maximum degree O(logd n). The main advantage of our spanner is that it can be maintained efficiently as the points move: Assuming the trajectories of the points can be described by boundeddegree polynomials, the number of topological changes to the spanner is O(n2 /εd−1 ), and using a supporting data structure of size O(n logd n) we can handle events in time O(logd+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. Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and problem complexity]: Nonnumerical Algorithms and Problems—Geometrical problems and computations General Terms Algorithms, Theory Keywords Geometric spanners, Kinetic data structures

• Type: Conference
• Year: 2009
• Where: COMPGEOM
• Authors: Mohammad Ali Abam, Mark de Berg
• Keywords: COMPGEOM 2009, Data Structures, Keywords Geometric Spanners, first Kinetic Spanner