@inproceedings{b1ecda618f204037b93c7d5f7a194a8f,

title = "From Proximity to Utility: A Voronoi Partition of Pareto Optima",

abstract = "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 or weights) are also considered. A cell in this diagram is then the loci of all clients that consider the same set of sites to be relevant. 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 this end, we derive several new technical results, which are of independent interest.",

keywords = "Backward analysis, Candidate diagram, Clarkson-Shor technique, Expected complexity, Pareto optima, Voronoi diagrams",

author = "Chang, {Hsien Chih} and Sariel Har-Peled and Benjamin Raichel",

year = "2015",

month = jun,

day = "1",

doi = "10.4230/LIPIcs.SOCG.2015.689",

language = "English (US)",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

pages = "689--703",

editor = "Janos Pach and Janos Pach and Lars Arge",

booktitle = "31st International Symposium on Computational Geometry, SoCG 2015",

note = "31st International Symposium on Computational Geometry, SoCG 2015 ; Conference date: 22-06-2015 Through 25-06-2015",

}