TY - JOUR

T1 - Approximating shortest paths on a convex polytope in three dimensions

AU - Agarwal, Pankaj K.

AU - Har-Peled, Sariel

AU - Sharir, Micha

AU - Varadarajan, Kasturi R.

PY - 1997/7

Y1 - 1997/7

N2 - 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.

AB - 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.

KW - Algorithms

KW - Approximation algorithms

KW - Convex polytopes

KW - Euclidean shortest paths

KW - Theory

UR - http://www.scopus.com/inward/record.url?scp=0031175637&partnerID=8YFLogxK

U2 - 10.1145/263867.263869

DO - 10.1145/263867.263869

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AN - SCOPUS:0031175637

SN - 0004-5411

VL - 44

SP - 567

EP - 584

JO - Journal of the ACM

JF - Journal of the ACM

IS - 4

ER -