On Cartesian trees and range minimum queries

Erik D. Demaine; Gad M. Landau; Oren Weimann

doi:10.1007/s00453-012-9683-x

On Cartesian trees and range minimum queries

Erik D. Demaine, Gad M. Landau, Oren Weimann

Department of Computer Science

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

Abstract

We present new results on Cartesian trees with applications in range minimum queries and bottleneck edge queries. We introduce a cache-oblivious Cartesian tree for solving the range minimum query problem, a Cartesian tree for the bottleneck edge query problem on trees and undirected graphs, and a proof that no Cartesian tree exists for the two-dimensional version of the range minimum query problem.

Original language	English
Pages (from-to)	610-625
Number of pages	16
Journal	Algorithmica
Volume	68
Issue number	3
DOIs	https://doi.org/10.1007/s00453-012-9683-x
State	Published - Mar 2014

Bibliographical note

Funding Information:
G.M. Landau is partially supported by the National Science Foundation Award 0904246, Israel Science Foundation grant 347/09, Yahoo, Grant No. 2008217 from the United States-Israel Binational Science Foundation (BSF) and DFG.

Keywords

Bottleneck paths
Cache-oblivious
Cartesian tree
Lowest common ancestor
Minimum spanning tree verification
Partial sums
Range minimum query

ASJC Scopus subject areas

General Computer Science
Computer Science Applications
Applied Mathematics

Access to Document

10.1007/s00453-012-9683-x

Cite this

@article{e44a442bda7c4ac18c9fdf5ff86a827c,

title = "On Cartesian trees and range minimum queries",

abstract = "We present new results on Cartesian trees with applications in range minimum queries and bottleneck edge queries. We introduce a cache-oblivious Cartesian tree for solving the range minimum query problem, a Cartesian tree for the bottleneck edge query problem on trees and undirected graphs, and a proof that no Cartesian tree exists for the two-dimensional version of the range minimum query problem.",

keywords = "Bottleneck paths, Cache-oblivious, Cartesian tree, Lowest common ancestor, Minimum spanning tree verification, Partial sums, Range minimum query",

author = "Demaine, \{Erik D.\} and Landau, \{Gad M.\} and Oren Weimann",

note = "Funding Information: G.M. Landau is partially supported by the National Science Foundation Award 0904246, Israel Science Foundation grant 347/09, Yahoo, Grant No. 2008217 from the United States-Israel Binational Science Foundation (BSF) and DFG. ",

year = "2014",

month = mar,

doi = "10.1007/s00453-012-9683-x",

language = "English",

volume = "68",

pages = "610--625",

journal = "Algorithmica",

issn = "0178-4617",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - On Cartesian trees and range minimum queries

AU - Demaine, Erik D.

AU - Landau, Gad M.

AU - Weimann, Oren

N1 - Funding Information: G.M. Landau is partially supported by the National Science Foundation Award 0904246, Israel Science Foundation grant 347/09, Yahoo, Grant No. 2008217 from the United States-Israel Binational Science Foundation (BSF) and DFG.

PY - 2014/3

Y1 - 2014/3

N2 - We present new results on Cartesian trees with applications in range minimum queries and bottleneck edge queries. We introduce a cache-oblivious Cartesian tree for solving the range minimum query problem, a Cartesian tree for the bottleneck edge query problem on trees and undirected graphs, and a proof that no Cartesian tree exists for the two-dimensional version of the range minimum query problem.

AB - We present new results on Cartesian trees with applications in range minimum queries and bottleneck edge queries. We introduce a cache-oblivious Cartesian tree for solving the range minimum query problem, a Cartesian tree for the bottleneck edge query problem on trees and undirected graphs, and a proof that no Cartesian tree exists for the two-dimensional version of the range minimum query problem.

KW - Bottleneck paths

KW - Cache-oblivious

KW - Cartesian tree

KW - Lowest common ancestor

KW - Minimum spanning tree verification

KW - Partial sums

KW - Range minimum query

UR - https://www.scopus.com/pages/publications/84897687861

U2 - 10.1007/s00453-012-9683-x

DO - 10.1007/s00453-012-9683-x

M3 - Article

AN - SCOPUS:84897687861

SN - 0178-4617

VL - 68

SP - 610

EP - 625

JO - Algorithmica

JF - Algorithmica

IS - 3

ER -

On Cartesian trees and range minimum queries

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this