A data structure for dynamic trees
Journal of Computer and System Sciences
Minimum Spanning Trees of Moving Points in the Plane
IEEE Transactions on Computers
Proximity problems on moving points
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Data structures for mobile data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
Voronoi Diagrams of Moving Points in the Plane
WG '91 Proceedings of the 17th International Workshop
Parametric and Kinetic Minimum Spanning Trees
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Davenport--Schinzel Sequences and Their Geometric Applications
Davenport--Schinzel Sequences and Their Geometric Applications
Kinetic data structures
Intersection reverse sequences and geometric applications
Journal of Combinatorial Theory Series A
Kinetic and dynamic data structures for convex hulls and upper envelopes
Computational Geometry: Theory and Applications
On minimum and maximum spanning trees of linearly moving points
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
A simple and efficient kinetic spanner
Computational Geometry: Theory and Applications
A kinetic triangulation scheme for moving points in the plane
Computational Geometry: Theory and Applications
Kinetic euclidean minimum spanning tree in the plane
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Kinetic and stationary point-set embeddability for plane graphs
GD'12 Proceedings of the 20th international conference on Graph Drawing
Kinetic data structures for all nearest neighbors and closest pair in the plane
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We construct a new proximity graph, called the Pie Delaunay graph, on a set of n points which is a super graph of Yaograph and Euclidean minimum spanning tree (EMST). We efficiently maintain the PieDelaunaygraph where the points are moving in the plane. We use the kinetic PieDelaunaygraph to create a kinetic data structure (KDS) for maintenance of the Yaograph and the EMST on a set of n moving points in 2-dimensional space. Assuming x and y coordinates of the points are defined by algebraic functions of at most degree s, the structure uses O(n) space, O(nlogn) preprocessing time, and processes O(n2λ2s+2(n)βs+2(n)) events for the Yaograph and O(n2λ2s+2(n)) events for the EMST, each in O(log2n) time. Here, λs(n)=nβs(n) is the maximum length of Davenport-Schinzel sequences of order s on n symbols. Our KDS processes nearly cubic events for the EMST which improves the previous bound O(n4) by Rahmati etal. [1].