Efficient embedding of binary trees in reconfigurable arrays with spanning optical buses

Optical bus based architectures have received much attention lately, and how to take advantage of the unique communication capabilities of such architectures in application development needs to be demonstrated. In this paper, we first describe an embedding of a binary tree into a Reconfigurable Array with Spanning Optical Buses (or RASOB), which achieves a near minimal expansion cost. We then describe an embedding of a large binary tree into a small RASOB, which achieves a near optimal load balance. In both embeddings, all packet transfers between parents and children in the binary trees can be accomplished in one bus cycle, which implies that the embeddings achieve an optimum dilation cost of 1.