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- Håstad, Johan, et al.
(författare)
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A smaller sleeping bag for a baby snake
- 2001
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Ingår i: Discrete & Computational Geometry. - : Springer Science and Business Media LLC. - 0179-5376 .- 1432-0444. ; 26:1, s. 173-181
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Tidskriftsartikel (refereegranskat)abstract
- By a sleeping bag for a baby snake in d dimensions we mean a subset of Rd which can cover, by rotation and translation, every curve of unit length. We construct sleeping bags which are smaller than any previously known in dimensions 3 and higher. In particular, we construct a three-dimensional sleeping bag of volume approximately 0.075803. For large d we construct d-dimensional sleeping bags with volume less than (cvlog d)d/d3d/2 for some constant c. To obtain the last result, we show that every curve of unit length in Rd lies between two parallel hyperplanes at distance at most C1d-3/2vlog d, for some constant c1.
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- Linusson, Svante, 1969-, et al.
(författare)
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Completing a k-1 assignment
- 2004
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We consider the distribution of the value of the optimal $k$-assignment in an $m \times n$-matrix, where the entries are independent exponential random variables with arbitrary rates. We give closed formulas for both the Laplace transform of this random variable and for its expected value under the condition that there is a zero-cost $k-1$-assignment.
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