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·ln(2) · 2n/n cross-edges. This improves previously known bisections with 4 · 2n/n cross-edges.
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© 1997 Springer-Verlag Berlin Heidelberg
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Feldmann, R., Monien, B., Mysliwietz, P., Tschöke, S. (1997). A better upper bound on the bisection width of de Bruijn networks. In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023485
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DOI: https://doi.org/10.1007/BFb0023485
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