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The Weber Point can be Found in Linear Time for Points in Biangular Configuration

Anderegg, Luzi and Cieliebak, Mark and Prencipe, Giuseppe (2003) The Weber Point can be Found in Linear Time for Points in Biangular Configuration. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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    The Weber point of a given point set $P$ is a point in the plane that minimizes the sum of all distances to the points in $P$. In general, the Weber point cannot be computed. However, if the points are in specific geometric patterns, then finding the Weber point is possible. We investigate the case of {\em biangular configurations}, where there is a center and two angles $\alpha$ and $\beta$ such that the angles w.r.t. the center between each two adjacent points is either $\alpha$ or $\beta$, and these angles alternate. We show that in this case the center of biangularity is the Weber point of the points, and that it can be found in time linear in the number of points.

    Item Type: Book
    Uncontrolled Keywords: weber point, minimum distance
    Subjects: Area01 - Scienze matematiche e informatiche > INF/01 - Informatica
    Divisions: Dipartimenti (until 2012) > DIPARTIMENTO DI INFORMATICA
    Depositing User: dott.ssa Sandra Faita
    Date Deposited: 17 Dec 2014 16:32
    Last Modified: 17 Dec 2014 16:32
    URI: http://eprints.adm.unipi.it/id/eprint/2089

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