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From Proximity to Utility: A Voronoi Partition of Pareto Optima $\renewcommand{\Re}{{\rm I\!\hspace{-0.025em} R}} \newcommand{\SetX}{\mathsf{X}} \newcommand{\VorX}[1]{\mathcal{V} \pth{#1}} \newcommand{\pth}[2][\!]{#1\left({#2}\right)}$

Hsien-Chih Chang, Sariel Har-Peled, and Benjamin Raichel.
We present an extension of Voronoi diagrams where not only the distance to the site is taken into account when considering which site the client is going to use, but additional attributes (i.e., prices) are also considered. A cell in this diagram is then the loci of all points that consider the same set of sites as relevant sites that the client might use. In particular, the precise site a client might use from this candidate set depends on parameters that might change between usages, and the candidate set lists all of the relevant sites. The resulting diagram is significantly more expressive than Voronoi diagrams, but naturally has the drawback that its complexity, even in the plane, might be quite high. Nevertheless, we show that if the attributes of the sites are drawn from the same distribution (note that the locations are fixed), then the expected complexity of the \candidate diagram is near linear. To derive this result, we derive several new technical results, which are of independent interest.
Talk: In SoCG 2015 (given by Hsien-Chih Chang).
Last modified: Thu Jul 16 13:51:58 CDT 2015