Long Monotone Paths in Line Arrangements
暂无分享,去创建一个
Abstract
We show how to construct an arrangement of n lines having a monotone path of
length
Ω(n2 – (d/\sqrt{log n})), where d > 0 is some constant, and thus
nearly settle the long standing question on monotone path length in line
arrangements.
[1] Adrian Dumitrescu. Monotone Paths in Line Arrangements with a Small Number of Directions , 2005, Discret. Comput. Geom..
[2] Jiří Matoušek. Lower bounds on the length of monotone paths in arrangements , 1991, Discret. Comput. Geom..
[3] Géza Tóth,et al. Monotone paths in line arrangement , 2001, SCG '01.
[4] Herbert Edelsbrunner,et al. Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.