Abstract.
A simple packing of a collection of rectangles contained in [0,1]2 is a disjoint subcollection such that each vertical line meets at most one rectangle of the packing. The wasted space of the packing is the surface of the area of the part of [0,1]2 not covered by the packing. We prove that for a certain number L, for all N≥2, the wasted space W N in an optimal simple packing of N independent uniformly distributed rectangles satisfies
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Work partially supported by an N.S.F. grant.
Mathematics Subject Classification (2000): 60D05
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Talagrand, M. Expected wasted space of optimal simple rectangle packing. Probab. Theory Relat. Fields 131, 145–153 (2005). https://doi.org/10.1007/s00440-003-0299-6
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DOI: https://doi.org/10.1007/s00440-003-0299-6
Key words or phrases:
- Random rectangle packing
- Interval packing
- Optimal packing