منابع مشابه
On Convex Body Chasing
A player moving in the plane is given a sequence of instructions of the following type: at step i a planar convex set Fi is specified, and the player has to move to a point in Fi. The player is charged for the distance traveled. We provide a strategy for the player which is competitive, i.e., for any sequence Fi the cost to the player is within a constant (multiplicative) factor of the "off-lin...
متن کاملChasing Convex Bodies and Functions
We consider three related online problems: Online Convex Optimization, Convex Body Chasing, and Lazy Convex Body Chasing. In Online Convex Optimization the input is an online sequence of convex functions over some Euclidean space. In response to a function, the online algorithm can move to any destination point in the Euclidean space. The cost is the total distance moved plus the sum of the fun...
متن کاملOn the symmetric average of a convex body
We introduce a new parameter, symmetric average, which measures the asymmetry of a given non-degenerated convex body K in Rn. Namely, sav(K) = infa∈intK ∫ Ka ‖ − x‖Ka dx/|K|, where |K| denotes the volume of K and Ka = K − a. We show that for polytopes sav(K) ≤ C ln N , where N is the number of facets of K. Moreover, in general n n+1 ≤ sav(K) < √ n and equality in the lower bound holds if and on...
متن کاملOn Approximation of a Three-dimensional Convex Body by Cylinders
New results on approximation of a convex body K ⊂ R3 by affine images of circular cylinders, parallelepipeds, hexagonal and octagonal regular (and some other) prisms are obtained. Two of the theorems obtained are as follows (V (K) denotes the volume of a body K ⊂ R3). Theorem 1. Let K be an arbitrary convex body in R3. There exists a regular octagonal prism an affine image of which is circumscr...
متن کاملOn the zone of the boundary of a convex body
We consider an arrangement A of n hyperplanes in R and the zone Z in A of the boundary of an arbitrary convex set in R in such an arrangement. We show that, whereas the combinatorial complexity of Z is known only to be O ( nd−1 log n ) [3], the outer part of the zone has complexity O ( nd−1 ) (without the logarithmic factor). Whether this bound also holds for the complexity of the inner part of...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1993
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02189324