Kinetic Spanners in ℝd

We present a new (1+ ε )-spanner for sets of n points in ℝ d . 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 bound...

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Bibliographic Details
Published inDiscrete & computational geometry Vol. 45; no. 4; pp. 723 - 736
Main Authors Abam, Mohammad Ali, de Berg, Mark
Format Journal Article
LanguageEnglish
Published New York Springer-Verlag 01.06.2011
Subjects
Combinatorics
Computational geometry
Computational Mathematics and Numerical Analysis
Data structures
Flight plans
Handles
Mathematics
Mathematics and Statistics
Spreads
Topology
Trajectories
Kinetic data structures
Geometric spanners
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Summary:We present a new (1+ ε )-spanner for sets of n points in ℝ d . 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 ( n log  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 ℝ d whose performance does not depend on the spread of the point set.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-011-9343-y