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Coverings

The algorithm to compute packings can be modified to get coverings. Assume, we have an interval tex2html_wrap_inline1697 such that tex2html_wrap_inline1699 . In this case, the spheres with centers in

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and radius r are covering all tex2html_wrap_inline587 and the spheres of radius tex2html_wrap_inline1707 are covering the whole space tex2html_wrap_inline555 . The density of the covering is

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propo315

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Remark.
This proposition implies that in order to get a good covering, the parameters r and tex2html_wrap_inline791 have to be chosen in such a way that tex2html_wrap_inline1749 is as homogeneous as possible. The computations for coverings are more involved as the computations for packings since the determination of the set includes a time-consuming sorting.



Oliver Knill
Mon Jun 22 17:57:55 CDT 1998