Constructing levels in arrangements and higher order Voronoi diagrams

P.K. Agarwal, M. Berg, de, J. Matousek, O. Schwarzkopf

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    72 Citations (Scopus)
    124 Downloads (Pure)

    Abstract

    We give simple randomized incremental algorithms for computing the Amk-level in an arrangement of n lines in the plane or in an arrangement of n planes in $\Reals^3$. The expected running time of our algorithms is $O(nk+n\alpha(n)\log n)$ for the planarcase and O(nk2 + n log3n) for the three-dimensional case. Both bounds are optimal unless k is very small. The algorithm generalizes to computing the Amk-level in an arrangement of discs or x-monotone Jordan curves in the plane. Our approach can also compute the k-level; this yields a randomized algorithm for computing the order-k Voronoi diagram of n points in the plane in expected time O(k(n-k)log n + n log3n).
    Original languageEnglish
    Pages (from-to)654-667
    JournalSIAM Journal on Computing
    Volume27
    Issue number3
    DOIs
    Publication statusPublished - 1998

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