Reporting points in halfspaces
Computational Geometry: Theory and Applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and 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
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Kinetic connectivity of rectangles
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Data structures for mobile data
Journal of Algorithms
Indexing moving points (extended abstract)
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Indexing the positions of continuously moving objects
SIGMOD '00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data
Maintaining approximate extent measures of moving points
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Kinetic maintenance of context-sensitive hierarchical representations for disjoint simple polygons
Proceedings of the eighteenth annual symposium on Computational geometry
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Direct visibility of point sets
ACM SIGGRAPH 2007 papers
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Let S be a set of n points moving on the real line. The kinetic sorting problem is to maintain a data structure on the set S that makes it possible to quickly generate a sorted list of the points in S, at any given time. We prove tight lower bounds for this problem, which show the following: with a subquadratic maintenance cost one cannot obtain any significant speed-up on the time needed to generate the sorted list (compared to the trivial O(n log n) time), even for linear motions.We also describe a kinetic data structure for so-called gift-wrapping queries on a set S of n moving points in the plane: given a point q and a line l through q such that all points from S lie on the same side of l, report which point pi ∈ S is hit first when l is rotated around q. Our KDS allows a trade-off between the query time and the maintenance cost: for any Q with 1 ≤ Q ≤ n, we can achieve O(Q log n) query time with a KDS that processes O(n2+ε/Q1+1/δ) events, where δ is the maximum degree of the polynomials describing the motions of the points. This allows us to reconstruct the convex hull quickly when the number of points on the convex hull is small. The structure also allows us to answer extreme-point queries (given a query direction ⃗d, what is the point from S that is extreme in direction ⃗d?) and convex-hull containment queries (given a query point q, is q inside the current convex hull?).