On the generalization of the pancake network

Abstract

In this study, we are particularly interested in one class of symmetric interconnection networks, namely the pancake graph, P/sub n/. Pancake graphs are especially attractive for distributed processing because they compare favorably with a hypercube of similar size. They have smaller degree and diameter than correspondingly large hypercubes. The one-sided pancake graph, P/sub n/, has been modeled as a Cayley graph on S/sub n/, the symmetric group of order n, while the two-sided pancake graph, 2P/sub n/, has been represented as a Cayley graph on the wreath product S/sub 2//spl bsol/S/sub n/. In this paper, we want to generalize the pancake graph, i.e., state the m-sided pancake flipping problem, and describe its graph as the m-sided pancake graph, mP/sub n/. Specifically, 1. we shall model the m-sided pancake graph, mP/sub n/ as Cayley graph on the wreath product of some finite groups; then, 2. we shall look into the degree, diameter and the routing protocol of the m-sided pancake graph, mP/sub n/; 3. we shall give the bounds for the diameters of mP/sub n/; and, 4. we shall give the diameters of 3P/sub n/ for 1 /spl les/ n /spl les/ 6.