Long monotone paths in line arrangements

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

doi:10.1007/s00454-004-1119-1

Long monotone paths in line arrangements

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

Research output: Contribution to journal › Article › peer-review

Abstract

We show how to construct an arrangement of n lines having a monotone path of length Ω(n^2-(d/√logn), where d > 0 is some constant, and thus nearly settle the long standing question on monotone path length in line arrangements.

Original language	English (US)
Pages (from-to)	167-176
Number of pages	10
Journal	Discrete and Computational Geometry
Volume	32
Issue number	2
DOIs	https://doi.org/10.1007/s00454-004-1119-1
State	Published - Sep 2004
Externally published	Yes

ASJC Scopus subject areas

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

Online availability

10.1007/s00454-004-1119-1

Library availability

Discover UIUC Full Text

Cite this

@article{ff48b26b73374b04a0032efc048a7e68,

title = "Long monotone paths in line arrangements",

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.",

author = "J{\'o}zsef Balogh and Oded Regev and Clifford Smyth and William Steiger and Mario Szegedy",

year = "2004",

month = sep,

doi = "10.1007/s00454-004-1119-1",

language = "English (US)",

volume = "32",

pages = "167--176",

journal = "Discrete and Computational Geometry",

issn = "0179-5376",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Long monotone paths in line arrangements

AU - Balogh, József

AU - Regev, Oded

AU - Smyth, Clifford

AU - Steiger, William

AU - Szegedy, Mario

PY - 2004/9

Y1 - 2004/9

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/4344580535

UR - https://www.scopus.com/pages/publications/4344580535#tab=citedBy

U2 - 10.1007/s00454-004-1119-1

DO - 10.1007/s00454-004-1119-1

M3 - Article

AN - SCOPUS:4344580535

SN - 0179-5376

VL - 32

SP - 167

EP - 176

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 2

ER -

Long monotone paths in line arrangements

Abstract

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this