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Publications [#235409] of Pankaj K. Agarwal

Papers Published

  1. Agarwal, PK; Aronov, B; Chan, TM; Sharir, M, On levels in arrangements of lines, segments, planes, and triangles, Discrete & Computational Geometry, vol. 19 no. 3 (1998), pp. 315-331, ISSN 0179-5376
    (last updated on 2017/12/11)

    Abstract:
    We consider the problem of bounding the complexity of the kth level in an arrangement of n curves or surfaces, a problem dual to, and an extension of, the well-known k-set problem. Among other results, we prove a new bound, O(nk5/3), on the complexity of the kth level in an arrangement of n planes in ℝ3, or on the number of k-sets in a set of n points in three dimensions, and we show that the complexity of the kth level in an arrangement of n line segments in the plane is O(n-√kα(n/k)), and that the complexity of the kth level in an arrangement of n triangles in 3-space is O(n2k5/6α(n/k)).

 

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