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Publications [#235413] of Pankaj K. Agarwal

Papers Published

  1. Agarwal, PK; Sharir, M, Pipes, cigars, and kreplach: The union of Minkowski sums in three dimensions, in Fifteenth Annual Symposium on Computational Geometry, Proceedings of the Annual Symposium on Computational Geometry (1999), pp. 143-153
    (last updated on 2018/10/20)

    Let Ω be a set of pairwise-disjoint polyhedral obstacles in R3 with a total of n vertices, and let B be a ball. We show that the combinatorial complexity of the free configuration space F of B amid Ω, i.e., the set of all placements of B at which B does not intersect any obstacle, is O(n2+ε), for any ε>0; the constant of proportionality depends on ε. This upper bound almost matches the known quadratic lower bound on the maximum possible complexity of F. We also present a randomized algorithm to compute the boundary of F whose expected running time is O(n2+ε), for any ε>0.
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