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Improved bounds on the crossing number of butterfly network

Abstract : We draw the r-dimensional butterfly network with 1 / 44r+O(r2r) crossings which improves the previous estimate given by Cimikowski (1996). We also give a lower bound which matches the upper bound obtained in this paper.
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Paul D. Manuel, Bharati Rajan, Indra Rajasingh, P. Vasanthi Beulah. Improved bounds on the crossing number of butterfly network. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2013, Vol. 15 no. 2 (2), pp.87--94. ⟨hal-00980758⟩

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