volume 33, issue 4, P687-697 2004
DOI: 10.1007/s00454-004-1106-6
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## Abstract: We give subquadratic bounds on the maximum length of an x-monotone path in an arrangement of n lines with at most C log log n directions, where C is a suitable constant. For instance, the maximum length of an x-monotone path in an arrangement of n lines having at most ten slopes is O(n 67/34 ). In particular, we get tight estimates for the case of lines having at most five directions, by showing that previous constructions-(n 3/2 ) for arrangements with four slopes and (n 5/3 ) for arrangements with five slop…

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