Sharp Bounds for Vertical Decompositions
of Linear Arrangements in Four Dimensions |
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Authors: | Email author" target="_blank">Vladlen?KoltunEmail author |
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Institution: | (1) Computer Science Division, University of California, Berkeley, CA 94720-1776 , USA |
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Abstract: | We prove tight and near-tight combinatorial complexity bounds for vertical decompositions of
arrangements of hyperplanes and 3-simplices in four dimensions. In particular, we prove a tight upper
bound of (n4) for the vertical decomposition of an arrangement of n hyperplanes in four
dimensions, improving the best previously known bound 8] by a logarithmic factor. We
also show that the complexity of the vertical decomposition of an arrangement of n 3-simplices in four
dimensions is O(n4 (n) log2 n), where (n) is the inverse Ackermann function,
improving the best previously known bound 2] by a near-linear factor. |
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Keywords: | |
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