Wafer packing is a process of combining multiple chip designs on the s
ame wafer such that the fabrication cost can be shared by several desi
gns and hence reduced. This technique is widely used for designs that
require a small number of dies or chips. It is essential to have compu
ter algorithms to decide how to allocate designs to wafers in order to
reduce the total fabrication cost. Based on different wafer fabricati
on techniques, two versions of the wafer packing problem are formulate
d. We study different variations for each version. We present algorith
ms to find optimal solutions for these variations which are polynomial
-time solvable. We also present heuristic algorithms for those proven
to be NP-hard. The effectiveness of the proposed algorithms is demonst
rated by experimental results.