Improved embeddings in POPS networks through stack-graph models

In 1996 MPPOI, Gravenstreter and Melhem presented optimal embeddings of ring and torus communications on the POPS architecture, for the case where the number of nodes (n) and the optical passive star (OPS) coupler degree (d) are powers of two. In the same conference, Bourdin, Ferreira and Marcus; see massively parallel multiprocessing using optical interconnections, San Antonio, USA, Oct, 1995, IEEE press; proposed stack-graphs as a good model for OPS-based architectures. In this paper we show that directed stack-complete graphs with loops (stack-K⁺_n for shown perfectly model POPS. As a consequence, we settle the question with respect to ring embeddings, presenting optimal embeddings for all values of n and d, based on Euler tours on K⁺_n. We also show how to optimally embeded Bruijn (B (g, D)) communications on POPS when g is the number of groups in the POPS topology, using the fact that K⁺_g is also a B (g, 1)