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Removing Depth-Order Cycles Among Triangles: An Efficient Algorithm Generating Triangular Fragments
[article]
2017
arXiv
pre-print
More than 25 years ago Chazelle et al. (FOCS 1991) studied the following question: Is it possible to cut any set of n lines in R^3 into a subquadratic number of fragments such that the resulting fragments admit a depth order? They proved an O(n^9/4) bound for the very special case of bipartite weavings of lines. Since then only little progress was made, until a recent breakthrough by Aronov and Sharir (STOC 2016) who showed that O(n^3/2polylog n) fragments suffice for any set of lines. In a
arXiv:1701.00679v2
fatcat:rluksjuvdnaa7ifnu2klnwxtha