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We address the complexity of computing the smallest-radius infinite cylinder that encloses an input set of n points in 3-space. We further report on experimental work involving an exact and a numerical strategy. A major topic of geometric optimization is to approximate point sets by simple geometric figures. This includes extensively studied planar problems… (More)

Let S be a set of n points in IR d , and let each p o i n t p of S have a p o s i t i v e 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 min p2S w(p) d(pp R) (resp. min p2S w(p) d(pp l)) is maximal. If all weights are one, this corresponds to computing a silo emanating from… (More)

This paper introduces the concept of precision-sensitive algorithms, in analogy to the well-known output-sensitive algorithms. We exploit this idea in studying the complexity of the 3-dimensional Euclidean shortest path problem. Speciically, we analyze an incremental approximation approach based on ideas in CSY], and show that this approach yields an… (More)

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 consider the problem of planning curvature constrained paths amidst polyg-onal obstacles, connecting given start and target conngurations. Let the critical curvature R c be the minimal curvature for which a constrained path exists. We describe an algorithm, which approximates the critical curvature and nds a corresponding path. Further, we give an… (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 2 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… (More)