Simulation of Binary Trees and X-Trees on Pyramid Networks

Traditionally, pyramid machines have been used for image processing problems. In this paper, we examine techniques for extending the use of pyramid networks. In particular, we show (1) every complete binary tree is a subgraph of its optimum pyramid, (2) the X-tree is not a subgraph of its optimum pyramid, but (3) every X-tree can be embedded into its optimum pyramid with dilation 2 and edge congestion 2, and (4) every binary tree can be embedded into a pyramid with constant dilation and constant expansion.