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

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(n3 2s(n2 )) for the number of the combinatorial changes of the EMST, where s(n)=s(n)/n and s(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 ).

• Type: Conference
• Year: 2010
• Where: CCCG
• Authors: Zahed Rahmati, Alireza Zarei
• Keywords: CCCG 2010, Combinatorial Changes, Computational Geometry, Euclidean Minimum Spanning Tree, Maximum Degree