Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Topologically sweeping an arrangement
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Algorithms for vertical and orthogonal L1 linear approximation of points
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Lower bounds on the length of monotone paths in arrangements
Discrete & Computational Geometry
Long monotone paths in line arrangements
Proceedings of the nineteenth annual symposium on Computational geometry
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We show that for any $n$ there is an arrangement of $n$ lines which co ntain an $x$-monotone path of length $\Omega(n^{7/4})$.