Abstract
We consider two on-line methods of covering the unit cube of Euclideand-space by sequences of cubes. The on-line restriction means that we are given the next cube from the sequence only after the preceding cube has been put in place without the possibility of changing the placement. The first method enables on-line covering of the unit cube by an arbitrary sequence of cubes whose total volume is at least 3...2 d −4. The second method is more complicated, but, asymptotically, asd tends to infinity, it yields an efficiency of the order of magnitude 2 d with factor 1. So, asymptotically, it is as good as the best possible non-on-line method of covering the unit cube by cubes.
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