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

نویسندگان

  • Zahed Rahmati
  • Alireza Zarei
چکیده

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 2dimensional 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(nβ2s(n )) 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(n).

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تاریخ انتشار 2010