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 computte for an infinite class of de Bruijn networks a bisection, that has asymptotically only 2 ln(2) 2~n /n cross-edges. This improves previously known bisections with 4 2~n /n cross-edges.
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