We analyze the number of tile types t, bins b, and stages necessary to
assemble n×n squares and scaled shapes in the staged tile assembly
model. For n×n squares, we prove O(b2logn−tb−tlogt+logtloglogb) stages suffice and
Ω(b2logn−tb−tlogt) are necessary for almost all n.
For shapes S with Kolmogorov complexity K(S), we prove
O(b2K(S)−tb−tlogt+logtloglogb)
stages suffice and Ω(b2K(S)−tb−tlogt) are necessary to
assemble a scaled version of S, for almost all S. We obtain similarly tight
bounds when the more powerful flexible glues are permitted.Comment: Abstract version appeared in ESA 201