Points Joined by Three Shortest Paths on Convex Surfaces
نویسندگان
چکیده
منابع مشابه
Computing Approximate Shortest Paths on Convex Polytopes1
The algorithms for computing a shortest path on a polyhedral surface are slow, complicated, and numerically unstable. We have developed and implemented a robust and efficient algorithm for computing approximate shortest paths on a convex polyhedral surface. Given a convex polyhedral surface P in R3, two points s, t ∈ P , and a parameter ε > 0, it computes a path between s and t on P whose lengt...
متن کاملGeneralized Source Shortest Paths on Polyhedral Surfaces
We present an algorithm for computing shortest paths and distances from a single generalized source (point, segment, polygonal chain or polygon) to any query point on a possibly non-convex polyhedral surface. The algorithm also handles the case in which polygonal chain or polygon obstacles on the polyhedral surface are allowed. Moreover, it easily extends to the case of several generalized sour...
متن کاملStochastic Shortest Paths Via Quasi-convex Maximization
We consider the problem of finding shortest paths in a graph with independent randomly distributed edge lengths. Our goal is to maximize the probability that the path length does not exceed a given threshold value (deadline). We give a surprising exact n n) algorithm for the case of normally distributed edge lengths, which is based on quasi-convex maximization. We then prove average and smoothe...
متن کاملApproximate Euclidean shortest paths amid convex obstacles
We develop algorithms and data structures for the approximate Euclidean shortest path problem amid a set P of k convex obstacles in R and R, with a total of n faces. The running time of our algorithms is linear in n, and the size and query time of our data structure are independent of n. We follow a “core-set” based approach, i.e., we quickly compute a small sketch Q of P whose size is independ...
متن کاملApproximate Shortest Paths and Geodesic Diameter on a Convex Polytope in Three Dimensions
Given a convex polytope P with n edges in R3, we present a relatively simple algorithm that preprocesses P in O(n) time, such that, given any two points s, t ∈ ∂P , and a parameter 0 < ε ≤ 1, it computes, in O((log n)/ε1.5 + 1/ε3) time, a distance 1P(s, t), such that dP(s, t) ≤ 1P(s, t) ≤ (1+ ε)dP(s, t), where dP(s, t) is the length of the shortest path between s and t on ∂P . The algorithm als...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1995
ISSN: 0002-9939
DOI: 10.2307/2161100