Approximating the weight of the Euclidean minimum spanning tree in sublinear time

Artur Czumaj; Funda Ergün; Lance Fortnow; Avner Magen; Ilan Newman; Ronitt Rubinfeld; Christian Sohler

doi:10.1137/S0097539703435297

Approximating the weight of the Euclidean minimum spanning tree in sublinear time

Artur Czumaj, Funda Ergün, Lance Fortnow, Avner Magen, Ilan Newman, Ronitt Rubinfeld, Christian Sohler

Department of Computer Science

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

Abstract

We consider the problem of computing the weight of a Euclidean minimum spanning tree for a set of n points in ℝ ^d. We focus on the setting where the input point set is supported by certain basic (and commonly used) geometric data structures that can provide efficient access to the input in a structured way. We present an algorithm that estimates with high probability the weight of a Euclidean minimum spanning tree of a set of points to within 1 + ε using only Õ(√n poly (1/ε)) queries for constant d. The algorithm assumes that the input is supported by a minimal bounding cube enclosing it, by orthogonal range queries, and by cone approximate nearest neighbor queries.

Original language	English
Pages (from-to)	91-109
Number of pages	19
Journal	SIAM Journal on Computing
Volume	35
Issue number	1
DOIs	https://doi.org/10.1137/S0097539703435297
State	Published - 2006

Keywords

Minimum spanning tree
Sublinear algorithms

ASJC Scopus subject areas

General Computer Science
General Mathematics

Access to Document

10.1137/S0097539703435297

Cite this

@article{318b74e2052c42b08bfe54a9528d5dd6,

title = "Approximating the weight of the Euclidean minimum spanning tree in sublinear time",

abstract = "We consider the problem of computing the weight of a Euclidean minimum spanning tree for a set of n points in ℝ d. We focus on the setting where the input point set is supported by certain basic (and commonly used) geometric data structures that can provide efficient access to the input in a structured way. We present an algorithm that estimates with high probability the weight of a Euclidean minimum spanning tree of a set of points to within 1 + ε using only {\~O}(√n poly (1/ε)) queries for constant d. The algorithm assumes that the input is supported by a minimal bounding cube enclosing it, by orthogonal range queries, and by cone approximate nearest neighbor queries.",

keywords = "Minimum spanning tree, Sublinear algorithms",

author = "Artur Czumaj and Funda Erg{\"u}n and Lance Fortnow and Avner Magen and Ilan Newman and Ronitt Rubinfeld and Christian Sohler",

year = "2006",

doi = "10.1137/S0097539703435297",

language = "English",

volume = "35",

pages = "91--109",

journal = "SIAM Journal on Computing",

issn = "0097-5397",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "1",

}

TY - JOUR

T1 - Approximating the weight of the Euclidean minimum spanning tree in sublinear time

AU - Czumaj, Artur

AU - Ergün, Funda

AU - Fortnow, Lance

AU - Magen, Avner

AU - Newman, Ilan

AU - Rubinfeld, Ronitt

AU - Sohler, Christian

PY - 2006

Y1 - 2006

N2 - We consider the problem of computing the weight of a Euclidean minimum spanning tree for a set of n points in ℝ d. We focus on the setting where the input point set is supported by certain basic (and commonly used) geometric data structures that can provide efficient access to the input in a structured way. We present an algorithm that estimates with high probability the weight of a Euclidean minimum spanning tree of a set of points to within 1 + ε using only Õ(√n poly (1/ε)) queries for constant d. The algorithm assumes that the input is supported by a minimal bounding cube enclosing it, by orthogonal range queries, and by cone approximate nearest neighbor queries.

AB - We consider the problem of computing the weight of a Euclidean minimum spanning tree for a set of n points in ℝ d. We focus on the setting where the input point set is supported by certain basic (and commonly used) geometric data structures that can provide efficient access to the input in a structured way. We present an algorithm that estimates with high probability the weight of a Euclidean minimum spanning tree of a set of points to within 1 + ε using only Õ(√n poly (1/ε)) queries for constant d. The algorithm assumes that the input is supported by a minimal bounding cube enclosing it, by orthogonal range queries, and by cone approximate nearest neighbor queries.

KW - Minimum spanning tree

KW - Sublinear algorithms

UR - http://www.scopus.com/inward/record.url?scp=33644586323&partnerID=8YFLogxK

U2 - 10.1137/S0097539703435297

DO - 10.1137/S0097539703435297

M3 - Article

AN - SCOPUS:33644586323

SN - 0097-5397

VL - 35

SP - 91

EP - 109

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

IS - 1

ER -

Approximating the weight of the Euclidean minimum spanning tree in sublinear time

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this