Kautz and de Bruijn graphs have a high degree of connectivity which makes
them ideal candidates for massively parallel computer network topologies. In
order to realize a practical computer architecture based on these graphs, it is
useful to have a means of constructing a large-scale system from smaller,
simpler modules. In this paper we consider the mathematical problem of
uniformly tiling a de Bruijn or Kautz graph. This can be viewed as a
generalization of the graph bisection problem. We focus on the problem of graph
tilings by a set of identical subgraphs. Tiles should contain a maximal number
of internal edges so as to minimize the number of edges connecting distinct
tiles. We find necessary and sufficient conditions for the construction of
tilings. We derive a simple lower bound on the number of edges which must leave
each tile, and construct a class of tilings whose number of edges leaving each
tile agrees asymptotically in form with the lower bound to within a constant
factor. These tilings make possible the construction of large-scale computing
systems based on de Bruijn and Kautz graph topologies.Comment: 29 pages, 11 figure