Long Monotone Paths in Line Arrangements

Authors:
József Balogh;Oded Regev;Clifford Smyth;William Steiger;Mario Szegedy
Affiliations:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA;EECS Department, University of California at Berkeley, Berkeley, CA 94720, USA;Department of Mathematical Sciences, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213, USA;Department of Computer Science, Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ 08854, USA;Department of Computer Science, Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ 08854, USA
Venue:
Discrete & Computational Geometry
Year:
2004

Citing 0
Cited 2

On some monotone path problems in line arrangements

Computational Geometry: Theory and Applications
On some monotone path problems in line arrangements

Computational Geometry: Theory and Applications

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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.