Linear-space algorithms for distance preserving embedding

Tetsuo Asano; Prosenjit Bose; Paz Carmi; Anil Maheshwari; Chang Shu; Michiel Smid; Stefanie Wuhrer

Linear-space algorithms for distance preserving embedding

Tetsuo Asano, Prosenjit Bose, Paz Carmi, Anil Maheshwari, Chang Shu, Michiel Smid, Stefanie Wuhrer

Research output: Contribution to conference › Paper › peer-review

2 Scopus citations

Abstract

The distance preserving graph embedding problem is to embed vertices of a given weighted graph into points in 2-dimensional Euclidean space so that for each edge the distance between their corresponding endpoints is as close to the weight of the edge as possible. If the given graph is complete, that is, if distance constraints are given as a full matrix, then principal coordinate analysis can solve it in polynomial time. A serious disadvantage is its quadratic space requirement. In this paper we develop linear-space algorithms for this problem. A key idea is to partition a set of n objects into disjoint subsets (clusters) of size O(√n) such that the minimum inter cluster distance is maximized among all possible such partitions.

Original language	English
Pages	185-188
Number of pages	4
State	Published - 1 Dec 2007
Externally published	Yes
Event	19th Annual Canadian Conference on Computational Geometry, CCCG 2007 - Ottawa, ON, Canada Duration: 20 Aug 2007 → 22 Aug 2007

Conference

Conference	19th Annual Canadian Conference on Computational Geometry, CCCG 2007
Country/Territory	Canada
City	Ottawa, ON
Period	20/08/07 → 22/08/07

ASJC Scopus subject areas

Geometry and Topology

Cite this

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title = "Linear-space algorithms for distance preserving embedding",

abstract = "The distance preserving graph embedding problem is to embed vertices of a given weighted graph into points in 2-dimensional Euclidean space so that for each edge the distance between their corresponding endpoints is as close to the weight of the edge as possible. If the given graph is complete, that is, if distance constraints are given as a full matrix, then principal coordinate analysis can solve it in polynomial time. A serious disadvantage is its quadratic space requirement. In this paper we develop linear-space algorithms for this problem. A key idea is to partition a set of n objects into disjoint subsets (clusters) of size O(√n) such that the minimum inter cluster distance is maximized among all possible such partitions.",

author = "Tetsuo Asano and Prosenjit Bose and Paz Carmi and Anil Maheshwari and Chang Shu and Michiel Smid and Stefanie Wuhrer",

year = "2007",

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day = "1",

language = "English",

pages = "185--188",

note = "19th Annual Canadian Conference on Computational Geometry, CCCG 2007 ; Conference date: 20-08-2007 Through 22-08-2007",

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T1 - Linear-space algorithms for distance preserving embedding

AU - Asano, Tetsuo

AU - Bose, Prosenjit

AU - Carmi, Paz

AU - Maheshwari, Anil

AU - Shu, Chang

AU - Smid, Michiel

AU - Wuhrer, Stefanie

PY - 2007/12/1

Y1 - 2007/12/1

N2 - The distance preserving graph embedding problem is to embed vertices of a given weighted graph into points in 2-dimensional Euclidean space so that for each edge the distance between their corresponding endpoints is as close to the weight of the edge as possible. If the given graph is complete, that is, if distance constraints are given as a full matrix, then principal coordinate analysis can solve it in polynomial time. A serious disadvantage is its quadratic space requirement. In this paper we develop linear-space algorithms for this problem. A key idea is to partition a set of n objects into disjoint subsets (clusters) of size O(√n) such that the minimum inter cluster distance is maximized among all possible such partitions.

AB - The distance preserving graph embedding problem is to embed vertices of a given weighted graph into points in 2-dimensional Euclidean space so that for each edge the distance between their corresponding endpoints is as close to the weight of the edge as possible. If the given graph is complete, that is, if distance constraints are given as a full matrix, then principal coordinate analysis can solve it in polynomial time. A serious disadvantage is its quadratic space requirement. In this paper we develop linear-space algorithms for this problem. A key idea is to partition a set of n objects into disjoint subsets (clusters) of size O(√n) such that the minimum inter cluster distance is maximized among all possible such partitions.

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M3 - Paper

AN - SCOPUS:67650000800

SP - 185

EP - 188

T2 - 19th Annual Canadian Conference on Computational Geometry, CCCG 2007

Y2 - 20 August 2007 through 22 August 2007

ER -

Linear-space algorithms for distance preserving embedding

Abstract

Conference

ASJC Scopus subject areas

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