Math @ Duke

Publications [#235599] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; Berg, MD; Matoušek, J; Schwarzkopf, O, Constructing Levels in Arrangements and Higher Order Voronoi Diagrams,
SIAM Journal on Computing, vol. 27 no. 3
(1998),
pp. 654667
(last updated on 2018/03/19)
Abstract: We give simple randomized incremental algorithms for computing the ≤κlevel in an arrangement of n lines in the plane or in an arrangement of n planes in ℝ3. The expected running time of our algorithms is O(nκ + nα(n) logn) for the planar case and O(nκ2 + nlog3n) for the threedimensional case. Both bounds are optimal unless κ is very small. The algorithm generalizes to computing the ≤κlevel in an arrangement of discs or xmonotone Jordan curves in the plane. Our approach can also compute the κlevel; this yields a randomized algorithm for computing the orderκ Voronoi diagram of n points in the plane in expected time O(κ(n  κ) log n + n log3 n).


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