Report B 00-04
We present efficient algorithms for the on-line q-adic covering of the unit interval by sequences of segments. The basic method guarantees the covering provided the total length of segments in a sequence is at least 1+2 · 1/q-1/q3. Other algorithms improve this estimate for q >= 6. The unit d-dimensional cube can only be on-line covered by arbitrary sequence of cubes of the total volume at least 2d + 5/3 + 5/3 · 2-d.
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