ISSN:
1432-0444
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract LetB be a compact convex body symmetric around0 in ℝ2 which has nonempty interior, i.e., the unit ball of a two-dimensional Minkowski space. The self-packing radiusρ(m,B) is the smallestt such thatt B can be packed withm translates of the interior ofB. Form≤6 we show that the self-packing radiusρ(m,B)=1+2/α(m,B) whereα(m,B) is the Minkowski length of the side of the largest equilateralm-gon inscribed inB (measured in the Minkowski metric determined byB). We showρ(6,B)=ρ(7,B)=3 for allB, and determine most of the largest and smallest values ofρ(m,B) form≤7. For allm we have $$\left( {\frac{m}{{\delta (B)}}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} - \frac{3}{2} \leqslant \rho (m,B) \leqslant \left( {\frac{m}{{\delta (B)}}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + 1,$$ whereδ(B) is the packing density ofB in ℝ2.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02293042
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