More on k-sets of finite sets in the plane
Discrete & Computational Geometry
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
Lower bounds on the length of monotone paths in arrangements
Discrete & Computational Geometry
Lectures on Discrete Geometry
Monotone paths in line arrangements
Computational Geometry: Theory and Applications
Long Monotone Paths in Line Arrangements
Discrete & Computational Geometry
Monotone Paths in Line Arrangements with a Small Number of Directions
Discrete & Computational Geometry
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We estimate the minimum length of a longest monotone path in an arrangement of n lines, where length counts the number of turns on the path. Estimates are also obtained for the case when length counts the number of visited vertices. Our bounds are asymptotically tight. When length is defined as the size of a convex/concave chain in the arrangement an exact bound is obtained.