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A smaller sleeping bag for a baby snake
KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.ORCID iD: 0000-0002-5379-345X
2001 (English)In: Discrete & Computational Geometry, ISSN 0179-5376, E-ISSN 1432-0444, Vol. 26, no 1, 173-181 p.Article in journal (Refereed) Published
Abstract [en]

By a sleeping bag for a baby snake in d dimensions we mean a subset of R-d 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 (c root logd)(d)/d(3d/2) for some constant c. To obtain the last result, we show that every curve of unit length in R-d lies between two parallel hyperplanes at distance at most c(1)d(-3/2)root logd, for some, constant c(1).

Place, publisher, year, edition, pages
2001. Vol. 26, no 1, 173-181 p.
Identifiers
URN: urn:nbn:se:kth:diva-20673ISI: 000168989000010OAI: oai:DiVA.org:kth-20673DiVA: diva2:339369
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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Håstad, JohanLinusson, Svante

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