Math @ Duke

Publications [#235593] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; HarPeled, S; Sharir, M; Varadarajan, KR, Approximating shortest paths on a convex polytope in three dimensions,
Journal of the ACM, vol. 44 no. 4
(1997),
pp. 567584
(last updated on 2018/03/19)
Abstract: Given a convex polytope P with n faces in ℝ3, points s, t ∈ ∂P, and a parameter 0 < ∈ ≤ 1, we present an algorithm that constructs a path on ∂P from s to t whose length is at most (1 + ∈)dP(s, t), where dP(s, t) is the length of the shortest path between s and t on ∂P. The algorithm runs in O(n log 1/∈ + 1/∈3) time, and is relatively simple. The running time is O(n + 1/∈3) if we only want the approximate shortest path distance and not the path itself. We also present an extension of the algorithm that computes approximate shortest path distances from a given source point on ∂P to all vertices of P.


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