**
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 2, pp. 537-549 (2002)
**

#
On-line Algorithms for the $q$-adic Covering of the Unit Interval and for Covering a Cube by Cubes

##
Marek Lassak

Instytut Matematyki i Fizyki ATR, Kaliskiego 7, 85-796 Bydgoszcz, Poland, e-mail: lassak@atr.bydgoszcz.pl

**Abstract:** We present efficient algorithms for the on-line $q$-adic covering of the unit interval by sequences of segments. The basic method guarantees covering provided the total length of segments is at least $1+ 2\cdot {1\over q} - {1\over q^3}$. Other algorithms improve this estimate for $q\geq 6$. The unit $d$-dimensional cube can be on-line covered by an arbitrary sequence of cubes whose total volume is at least $2^d+{5\over 3}+{5\over 3}\cdot 2^{-d}$.

**Classification (MSC2000):** 52C17

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number]

*
© 2002 ELibM for
the EMIS Electronic Edition
*