Math @ Duke

Publications [#235427] of Pankaj K. Agarwal
Papers Published
 Varadarajan, KR; Agarwal, PK, Approximating shortest paths on a nonconvex polyhedron,
Siam Journal on Computing, vol. 30 no. 4
(2000),
pp. 13211340, ISSN 00975397
(last updated on 2018/09/25)
Abstract: We present an approximation algorithm that, given the boundary P of a simple, nonconvex polyhedron in ℝ3 and two points s and t on P, constructs a path on P between s and t whose length is at most 7(1 + ε)dP(s, t), where dP(s, t) is the length of the shortest path between s and t on P, and ε > 0 is an arbitrarily small positive constant. The algorithm runs in O(n5/3 log5/3 n) time, where n is the number of vertices in P. We also present a slightly faster algorithm that runs in O(n8/5 log8/5 n) time and returns a path whose length is at most 15(1 + ε)dP(s, t). © 2000 Society for Industrial and Applied Mathematics.


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