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Abstract: Let $G$ be a possibly disconnected planar subdivision and let $D$ be aprobability measure over $\R^2$. The current paper shows how to preprocess$G,D$ into an On size data structure that can answer planar point locationqueries over $G$. The expected query time of this data structure, for a querypoint drawn according to $D$, is $OH+1$, where $H$ is a lower bound on theexpected query time of any linear decision tree for point location in $G$. Thisextends the results of Collette et al 2008, 2009 from connected planarsubdivisions to disconnected planar subdivisions. A version of this structure,when combined with existing results on succinct point location, provides asuccinct distribution-sensitive point location structure.



Autor: Prosenjit Bose, Luc Devroye, Karim Douieb, Vida Dujmovic, James King, Pat Morin

Fuente: https://arxiv.org/







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