Linear approximation of simple objects

Jean Marc Robert, Godfried Toussaint

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Let S be a set of m convex polygons in the plane with a total number of n vertices. Each polygon has a positive weight. This paper presents algorithms to solve the weighted minmax approximation and the weighted minsum approximation problems. For the first problem, a line minimizing the maximum weighted distance to the polygons can be found in O(n2 log n) time and O(n2) space. The time and space complexities can be reduced to O(n log n) and O(n), respectively, when the weights are equal. For the second problem, a line minimizing the sum of the weighted distances to the polygons can be found in O(n2 log n) time and O(n) space. For both problems, we also obtain similar results for sets of n circles or line segments.

Original languageEnglish (US)
Title of host publicationSTACS 1992 - 9th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings
PublisherSpringer-Verlag
Pages233-244
Number of pages12
ISBN (Print)9783540552109
StatePublished - Jan 1 1992
Event9th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1992 - Cachan, France
Duration: Feb 13 1992Feb 15 1992

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume577 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other9th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1992
CountryFrance
CityCachan
Period2/13/922/15/92

Fingerprint

Linear Approximation
Polygon
Weighted Approximation
Line
Convex polygon
Space Complexity
Approximation Problem
Line segment
Min-max
Time Complexity
Circle
Approximation
Object

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Robert, J. M., & Toussaint, G. (1992). Linear approximation of simple objects. In STACS 1992 - 9th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings (pp. 233-244). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 577 LNCS). Springer-Verlag.

Linear approximation of simple objects. / Robert, Jean Marc; Toussaint, Godfried.

STACS 1992 - 9th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings. Springer-Verlag, 1992. p. 233-244 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 577 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Robert, JM & Toussaint, G 1992, Linear approximation of simple objects. in STACS 1992 - 9th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 577 LNCS, Springer-Verlag, pp. 233-244, 9th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1992, Cachan, France, 2/13/92.
Robert JM, Toussaint G. Linear approximation of simple objects. In STACS 1992 - 9th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings. Springer-Verlag. 1992. p. 233-244. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Robert, Jean Marc ; Toussaint, Godfried. / Linear approximation of simple objects. STACS 1992 - 9th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings. Springer-Verlag, 1992. pp. 233-244 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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