Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
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
On Levels in Arrangements of Curves, II: A Simple Inequality and Its Consequences
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Out-of-order event processing in kinetic data structures
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Kinetic algorithms via self-adjusting computation
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
An experimental analysis of self-adjusting computation
ACM Transactions on Programming Languages and Systems (TOPLAS)
Self-adjusting computation with Delta ML
AFP'08 Proceedings of the 6th international conference on Advanced functional programming
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Let S be a set of n moving points in the plane. We present a kinetic and dynamic (randomized) data structure for maintaining the convex hull of S. The structure uses O(n) space, and processes an expected number of O(n2βs+2(n)log n) critical events, each in O(log2n) expected time, including O(n) insertions, deletions, and changes in the flight plans of the points. Here s is the maximum number of times where any specific triple of points can become collinear, βs(q)=λs(q) / q, and λs(q) is the maximum length of Davenport-Schinzel sequences of order s on n symbols. Compared with the previous solution of Basch et al.[2], our structure uses simpler certificates, uses roughly the same resources, and is also dynamic.