Long monotone paths in line arrangements

József Balogh, Oded Regev, Clifford Smyth, William Steiger, Mario Szegedy

Research output: Contribution to journalArticle

Abstract

We show how to construct an arrangement of n lines having a monotone path of length Ω(n2-(d/√logn), where d > 0 is some constant, and thus nearly settle the long standing question on monotone path length in line arrangements.

Original languageEnglish (US)
Pages (from-to)167-176
Number of pages10
JournalDiscrete and Computational Geometry
Volume32
Issue number2
StatePublished - 2004

Fingerprint

Arrangement
Monotone
Path
Line
Path Length

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Discrete Mathematics and Combinatorics
  • Geometry and Topology

Cite this

Balogh, J., Regev, O., Smyth, C., Steiger, W., & Szegedy, M. (2004). Long monotone paths in line arrangements. Discrete and Computational Geometry, 32(2), 167-176.

Long monotone paths in line arrangements. / Balogh, József; Regev, Oded; Smyth, Clifford; Steiger, William; Szegedy, Mario.

In: Discrete and Computational Geometry, Vol. 32, No. 2, 2004, p. 167-176.

Research output: Contribution to journalArticle

Balogh, J, Regev, O, Smyth, C, Steiger, W & Szegedy, M 2004, 'Long monotone paths in line arrangements', Discrete and Computational Geometry, vol. 32, no. 2, pp. 167-176.
Balogh J, Regev O, Smyth C, Steiger W, Szegedy M. Long monotone paths in line arrangements. Discrete and Computational Geometry. 2004;32(2):167-176.
Balogh, József ; Regev, Oded ; Smyth, Clifford ; Steiger, William ; Szegedy, Mario. / Long monotone paths in line arrangements. In: Discrete and Computational Geometry. 2004 ; Vol. 32, No. 2. pp. 167-176.
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