Abstract
We discuss in this paper a method of finding skyline or non-dominated points in a set P of n points with respect to a set S of m sites. A point p i ∈ P is non-dominated if and only if for each p j ∈ P, \(j \not= i\), there exists at least one point s ∈ S that is closer to p i than p j . We reduce this problem of determining non-dominated points to the problem of finding sites that have non-empty cells in an additively weighted Voronoi diagram under convex distance function. The weights of the said Voronoi diagram are derived from the co-ordinates of the points of P and the convex distance function is derived from S. In the 2-dimensional plane, this reduction gives a O((m + n)logm + n logn)-time randomized incremental algorithm to find the non-dominated points.
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Bhattacharya, B., Bishnu, A., Cheong, O., Das, S., Karmakar, A., Snoeyink, J. (2010). Computation of Non-dominated Points Using Compact Voronoi Diagrams. In: Rahman, M.S., Fujita, S. (eds) WALCOM: Algorithms and Computation. WALCOM 2010. Lecture Notes in Computer Science, vol 5942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11440-3_8
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DOI: https://doi.org/10.1007/978-3-642-11440-3_8
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