STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Kinetic data structures: a state of the art report
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
On deletion in Delaunay triangulations
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Data structures for mobile data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Algorithmic issues in modeling motion
ACM Computing Surveys (CSUR)
Deformable spanners and applications
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
A computational framework for incremental motion
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Dense Point Sets Have Sparse Delaunay Triangulations or “... But Not Too Nasty”
Discrete & Computational Geometry
Star splaying: an algorithm for repairing delaunay triangulations and convex hulls
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Kinetic data structures in practice
Kinetic data structures in practice
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Untangling triangulations through local explorations
Proceedings of the twenty-fourth annual symposium on Computational geometry
Multi-dimensional online tracking
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Maintaining Nets and Net Trees under Incremental Motion
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Filtering relocations on a Delaunay triangulation
SGP '09 Proceedings of the Symposium on Geometry Processing
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Kinetic 2-centers in the black-box model
Proceedings of the twenty-ninth annual symposium on Computational geometry
Competitive query strategies for minimising the ply of the potential locations of moving points
Proceedings of the twenty-ninth annual symposium on Computational geometry
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Over the past decade, the kinetic-data-structures framework has become the standard in computational geometry for dealing with moving objects. A fundamental assumption underlying the framework is that the motions of the objects are known in advance. This assumption severely limits the applicability of KDSs. We study KDSs in the black-box model, which is a hybrid of the KDS model and the traditional time-slicing approach. In this more practical model we receive the position of each object at regular time steps and we have an upper bound on dmax, the maximum displacement of any point in one time step. We study the maintenance of the convex hull and the Delaunay triangulation of a planar point set P in the black-box model, under the following assumption on dmax: there is some constant k such that for any point p ∑ P the disk of radius dmax contains at most k points. We analyze our algorithms in terms of ∑k , the so-called k-spread of P. We show how to update the convex hull at each time step in O(k∑k log2 n) amortized time. For the Delaunay triangulation our main contribution is an analysis of the standard edge-flipping approach; we show that the number of flips is O(k2 ∑k2) at each time step.