A Better Upper Bound on the Bisection Width of de Bruijn Networks (Extended Abstract)

. We approach the problem of bisectioning the de Bruijn network into two parts of equal size and minimal number of edges connecting the two parts (cross-edges). We introduce a general method that is based on required substrings. A partition is defined by taking as one part all the nodes containing a certain string and as the other part all the other nodes. This leads to good bisections for a large class of dimensions. The analysis of this method for a special kind of substrings enables us to compute for an infinite class of de Bruijn networks a bisection, that has asymptotically only 2 \Delta ln(2) \Delta 2 n =n cross-edges. This improves previously known bisections with 4 \Delta 2 n =n cross-edges. 1 Introduction The graph-bisection-problem is one of the best studied problems in graph theory. It has various important applications, for example in VLSI-layout [Len94] and in parallel computing [Lei92]. Given a graph G = (V; E) the bisection width fi(G) is the minimal number of edge..