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Papadimitriou's approximation approach to the Euclidean shortest path (ESP) problem in 3-space is revisited. As this problem is NP-hard, his approach represents an important step towards practical algorithms. Unfortunately, there are non-trivial gaps in the original description. Besides giving a complete treatment, we also give an alternative to his(More)
We examine shortest path planning Jurgen Sellen * FB 14 ~ Informatik Universit at des Saarlandes 151150, 66041 Saarbrucken, Germany under a direct ion weighted Euclidean metric, motivated b y the problem of finding opt imal routes for sailboats. We show that f o r piecewise linear weight functions the shortest path an the unrestricted plane always consists(More)
Let S be a set of n points in IR and let each point p of S have a positive weight w p We consider the problem of computing a ray R emanating from the origin resp a line l through the origin such that minp S w p d p R resp minp S w p d p l is maximal If all weights are one this corresponds to computing a silo emanating from the origin resp a cylinder whose(More)
This paper addresses the complexity of computing the smallest-radius infinite cylinder that encloses an input set of n points in 3-space. We show that the problem can be solved in time O(n 4 log O(1) n) in an algebraic complexity model. We also achieve a time of O(n 4 L⋅μ(L)) in a bit complexity model where L is the maximum bit size of input numbers and(More)
Let S be a set of n points in the plane, and let each point p of S have a positive weight w(p). We consider the problem of positioning a point x inside a compact region R ⊆ R such that min{ w(p)−1 · d(x, p) ; p ∈ S } is maximized. Based on the parametric search paradigm, we give the first subquadratic algorithms for this problem, with running time O(n log(More)