ALCOMFT-TR-03-7

Alexander Tiskin
Packing tripods: A computational approach
Warwick. Work packages 4 and 5. June 2003.

Abstract: In 1994, S. K. Stein and S. Szab\'o posed a problem concerning simple three-dimensional polyominoes, called ``tripods''. How densely can one fill a cube of size n with non-overlapping tripods? Following Stein, we denote by f(n) the maximum size of such a tripod packing. The best previously known lower bound for Stein's function is f(n)=Omega(n^1.5235). We show that this lower bound can be improved to Omega(n^1.5287). We also make some conjectures on the structure of good packings, and suggest possible further improvements to our experiments.

Postscript file: ALCOMFT-TR-03-7.ps.gz (72 kb).