dc.contributor.author Chew, L. Paul en_US dc.date.accessioned 2007-04-23T16:29:25Z dc.date.available 2007-04-23T16:29:25Z dc.date.issued 1993-05 en_US dc.identifier.citation http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR93-1348 en_US dc.identifier.uri https://hdl.handle.net/1813/6118 dc.description.abstract Given a set of $n$ moving points in the plane, how many topological changes occur in the Voronoi diagram of the points? If each point has constant velocity then there is an upper bound of $O(n^{3})$ [Guibas, Mitchell and Roos] and an easy lower bound of $\Omega(n^{2})$. It is widely believed that the true upper bound should be close to $O(n^{2})$. We show this belief to be true for the case of Voronoi diagrams based on the $L_{1}$ (or $L_{\infty}$) metric; the number of changes is shown to be $O(n^{2} \alpha (n))$ where $\alpha(n)$ grows so slowly it is effectively a small constant for all reasonable values of $n$. en_US dc.format.extent 664505 bytes dc.format.extent 159046 bytes dc.format.mimetype application/pdf dc.format.mimetype application/postscript dc.language.iso en_US en_US dc.publisher Cornell University en_US dc.subject computer science en_US dc.subject technical report en_US dc.title Near-Quadratic Bounds for the $L_{1}$ Voronoi Diagram of Moving Points en_US dc.type technical report en_US
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