On some monotone path problems in line arrangements

Authors:
Adrian Dumitrescu
Affiliations:
Computer Science, University of Wisconsin-Milwaukee, 3200 N. Cramer Street, Milwaukee, WI
Venue:
Computational Geometry: Theory and Applications
Year:
2005

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Abstract

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.