Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Adding range restriction capability to dynamic data structures
Journal of the ACM (JACM)
There is a planar graph almost as good as the complete graph
SCG '86 Proceedings of the second annual symposium on Computational geometry
Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Approximating the complete Euclidean graph
No. 318 on SWAT 88: 1st Scandinavian workshop on algorithm theory
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Proximity problems on moving points
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
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
Data structures for mobile data
Journal of Algorithms
A segment-tree based kinetic BSP
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Computational Geometry: Theory and Applications - Special issue on the 14th Canadian conference on computational geometry — CCCG02
Deformable spanners and applications
Computational Geometry: Theory and Applications
Geometric Spanner Networks
Kinetic KD-trees and longest-side KD-trees
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Fully dynamic geometric spanners
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Improved algorithms for fully dynamic geometric spanners and geometric routing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
A simple and efficient kinetic spanner
Proceedings of the twenty-fourth 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/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 bounded-degree polynomials, the number of topological changes to the spanner is O(n2/εd-1), and using a supporting data structure of size O(n logdn) we can handle events in time O(logd+1n). 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.