Evenly Distributed Depth is the Worst for Distributed Snooping

In the purely object-parallel approach to multiprocessor rendering, each processor is assigned responsibility to render a subset of the graphics database. When rendering is complete, pixels from the processors must be merged and globally z-bu ered. On an arbitrary multiprocessor interconnection network, the straightforward algorithm for pixel merging requires dA total network bandwidth per frame, where d is the depth complexity of the scene and A is the area of the screen or window. In another paper we have presented a distributed snooping algorithm for pixel merging that requires log( d)A expected network bandwidth per frame. In that paper, to simplify the analysis we required the assumption that depth is \evenly" distributed over the screen, and we claimed that this assumption represented a worst-case for expected tra c. In the current paper we prove this claim.