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Combinatorial changes of euclidean minimum spanning tree of moving points in the plane

Rahmati, Z ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. Publisher: 2010
  3. Abstract:
  4. In this paper, we enumerate the number of combinatorial changes of the the Euclidean minimum spanning tree (EMST) of a set of n moving points in 2- dimensional space. We assume that the motion of the points in the plane, is defined by algebraic functions of maximum degree s of time. We prove an upper bound of O(n3β2s(n2)) for the number of the combinatorial changes of the EMST, where βs(n)= λs(n)/n and λs(n) is the maximum length of Davenport-Schinzel sequences of order s on n symbols which is nearly linear in n. This result is an O(n) improvement over the previously trivial bound of O(n4)
  5. Keywords:
  6. 2 - Dimensional ; Algebraic functions ; Davenport-Schinzel sequences ; Euclidean minimum spanning trees ; Maximum degree ; Upper Bound ; Computational geometry
  7. Source: Proceedings of the 22nd Annual Canadian Conference on Computational Geometry, CCCG 2010, 9 August 2010 through 11 August 2010, Winnipeg, MB ; 2010 , Pages 43-45
  8. URL: http://cccg.ca/proceedings/2010/paper14.pdf