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Kinetic Euclidean minimum spanning tree in the plane

Rahmati, Z ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1016/j.jda.2012.04.009
  3. Publisher: Elsevier , 2012
  4. Abstract:
  5. 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
  6. Keywords:
  7. Algebraic functions ; Combinatorial structures ; Delaunay triangulation ; Euclidean minimum spanning trees ; Kinetic data structure ; Maximum degree ; Monitoring change ; Performance parameters ; Preprocessing time ; Time stamps ; Data structures ; Triangulation ; Kinetics
  8. Source: Journal of Discrete Algorithms ; Volume 16 , October , 2012 , Pages 2-11 ; 15708667 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S1570866712000639