The Fitting Line Problem in the Laguerre Geometry

François Anton; Sergey Bereg

The Fitting Line Problem in the Laguerre Geometry

François Anton
, Sergey Bereg

University of Texas at Dallas
Unknown

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Abstract

We address the problem of computing the fitting line of a set of circles in the Laguerre metric, that minimizes the distance to the farthest circle. To solve the fitting line problem we introduce a generalization of the concept of the width of a set of points using the Laguerre metric. We also present an efficient algorithm for finding the fitting line of a set of circles using minimization diagrams with running time O(n^2+epsilon), for any epsilon greater than 0.

Original language	English
Title of host publication	Proceedings of the Sixteenth Canadian Conference on Computational Geometry
Publication date	2004
Pages	166-169
Publication status	Published - 2004
Externally published	Yes
Event	16th Canadian Conference on Computational Geometry - Montreal, Canada Duration: 9 Aug 2004 → 11 Aug 2004 Conference number: 16 http://www.cccg.ca/proceedings/2004/

Conference

Conference	16th Canadian Conference on Computational Geometry
Number	16
Country/Territory	Canada
City	Montreal
Period	09/08/2004 → 11/08/2004
Internet address	http://www.cccg.ca/proceedings/2004/

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@inproceedings{da965a9b88504e308a1467d2bb8f94d5,

title = "The Fitting Line Problem in the Laguerre Geometry",

abstract = "We address the problem of computing the fitting line of a set of circles in the Laguerre metric, that minimizes the distance to the farthest circle. To solve the fitting line problem we introduce a generalization of the concept of the width of a set of points using the Laguerre metric. We also present an efficient algorithm for finding the fitting line of a set of circles using minimization diagrams with running time O(n\textasciicircum{}2+epsilon), for any epsilon greater than 0.",

author = "Fran{\c c}ois Anton and Sergey Bereg",

year = "2004",

language = "English",

pages = "166--169",

booktitle = "Proceedings of the Sixteenth Canadian Conference on Computational Geometry",

note = "16th Canadian Conference on Computational Geometry, CCCG 2004 ; Conference date: 09-08-2004 Through 11-08-2004",

url = "http://www.cccg.ca/proceedings/2004/",

}

TY - GEN

T1 - The Fitting Line Problem in the Laguerre Geometry

AU - Anton, François

AU - Bereg, Sergey

N1 - Conference code: 16

PY - 2004

Y1 - 2004

N2 - We address the problem of computing the fitting line of a set of circles in the Laguerre metric, that minimizes the distance to the farthest circle. To solve the fitting line problem we introduce a generalization of the concept of the width of a set of points using the Laguerre metric. We also present an efficient algorithm for finding the fitting line of a set of circles using minimization diagrams with running time O(n^2+epsilon), for any epsilon greater than 0.

AB - We address the problem of computing the fitting line of a set of circles in the Laguerre metric, that minimizes the distance to the farthest circle. To solve the fitting line problem we introduce a generalization of the concept of the width of a set of points using the Laguerre metric. We also present an efficient algorithm for finding the fitting line of a set of circles using minimization diagrams with running time O(n^2+epsilon), for any epsilon greater than 0.

M3 - Article in proceedings

SP - 166

EP - 169

BT - Proceedings of the Sixteenth Canadian Conference on Computational Geometry

T2 - 16th Canadian Conference on Computational Geometry

Y2 - 9 August 2004 through 11 August 2004

ER -

The Fitting Line Problem in the Laguerre Geometry

Abstract

Conference

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