Data structures and network algorithms
Data structures and network algorithms
Randomized incremental construction of Delaunay and Voronoi diagrams
Proceedings of the seventeenth international colloquium on Automata, languages and programming
Minimum Spanning Trees of Moving Points in the Plane
IEEE Transactions on Computers
On the randomized construction of the Delaunay tree
Theoretical Computer Science
Proximity problems on moving points
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Computational geometry in C (2nd ed.)
Computational geometry in C (2nd ed.)
Data structures for mobile data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
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
A dynamic data structure for 3-d convex hulls and 2-d nearest neighbor queries
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Kinetic and dynamic data structures for convex hulls and upper envelopes
Computational Geometry: Theory and Applications
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
On levels in arrangements of curves, iii: further improvements
Proceedings of the twenty-fourth annual symposium on Computational geometry
On minimum and maximum spanning trees of linearly moving points
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Kinetic and dynamic data structures for closest pair and all nearest neighbors
ACM Transactions on Algorithms (TALG)
A simple and efficient kinetic spanner
Computational Geometry: Theory and Applications
Fast euclidean minimum spanning tree: algorithm, analysis, and applications
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
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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This paper presents a kinetic data structure (KDS) for maintenance of the Euclidean minimum spanning tree (EMST) on a set of moving points in 2-dimensional space. For a set of n points moving in the plane we build a KDS of size O(n) in O(nlogn) preprocessing time by which the EMST is maintained efficiently during the motion. This is done by applying the required changes to the combinatorial structure of the EMST which is changed in discrete timestamps. We assume that the motion of the points, i.e. x and y coordinates of the points, are defined by algebraic functions of constant maximum degree. In terms of the KDS performance parameters, our KDS is responsive, local, and compact. The presented KDS is based on monitoring changes of the Delaunay triangulation of the points and edge-length changes of the edges of the current Delaunay triangulation.