On some geometric selection and optimization problems via sorted matrices

Alex Glozman; Klara Kedem; Gregory Shpitalnik

doi:10.1007/3-540-60220-8_48

On some geometric selection and optimization problems via sorted matrices

Alex Glozman, Klara Kedem, Gregory Shpitalnik

Department of Computer Science

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

12 Scopus citations

Abstract

In this paper we apply the selection and optimization technique of Fredrickson and Johnson to a number of geometric selection and optimization problems, some of which have previously been solved by parametric search, and provide efficient and simple algorithms. Our technique improves the solutions obtained by parametric search by a log n factor. For example, we apply the technique to the two-line-center problem, where we want to find two strips that cover a given set S of n points in the plane, so as to minimize the width of the largest of the two strips.

Original language	English
Title of host publication	Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings
Editors	Selim G. Akl, Frank Dehne, Jörg-Rüdiger Sack, Nicola Santoro
Publisher	Springer Verlag
Pages	26-37
Number of pages	12
ISBN (Print)	3540602208, 9783540602200
DOIs	https://doi.org/10.1007/3-540-60220-8_48
State	Published - 1 Jan 1995
Event	4th Workshop on Algorithms and Data Structures, WADS 1995 - Kingston, Canada Duration: 16 Aug 1995 → 18 Aug 1995

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	955
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	4th Workshop on Algorithms and Data Structures, WADS 1995
Country/Territory	Canada
City	Kingston
Period	16/08/95 → 18/08/95

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/3-540-60220-8_48

Cite this

Glozman, A., Kedem, K., & Shpitalnik, G. (1995). On some geometric selection and optimization problems via sorted matrices. In S. G. Akl, F. Dehne, J.-R. Sack, & N. Santoro (Eds.), Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings (pp. 26-37). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 955). Springer Verlag. https://doi.org/10.1007/3-540-60220-8_48

Glozman, Alex ; Kedem, Klara ; Shpitalnik, Gregory. / On some geometric selection and optimization problems via sorted matrices. Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings. editor / Selim G. Akl ; Frank Dehne ; Jörg-Rüdiger Sack ; Nicola Santoro. Springer Verlag, 1995. pp. 26-37 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "In this paper we apply the selection and optimization technique of Fredrickson and Johnson to a number of geometric selection and optimization problems, some of which have previously been solved by parametric search, and provide efficient and simple algorithms. Our technique improves the solutions obtained by parametric search by a log n factor. For example, we apply the technique to the two-line-center problem, where we want to find two strips that cover a given set S of n points in the plane, so as to minimize the width of the largest of the two strips.",

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Glozman, A, Kedem, K & Shpitalnik, G 1995, On some geometric selection and optimization problems via sorted matrices. in SG Akl, F Dehne, J-R Sack & N Santoro (eds), Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 955, Springer Verlag, pp. 26-37, 4th Workshop on Algorithms and Data Structures, WADS 1995, Kingston, Canada, 16/08/95. https://doi.org/10.1007/3-540-60220-8_48

On some geometric selection and optimization problems via sorted matrices. / Glozman, Alex; Kedem, Klara; Shpitalnik, Gregory.
Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings. ed. / Selim G. Akl; Frank Dehne; Jörg-Rüdiger Sack; Nicola Santoro. Springer Verlag, 1995. p. 26-37 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 955).

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

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N2 - In this paper we apply the selection and optimization technique of Fredrickson and Johnson to a number of geometric selection and optimization problems, some of which have previously been solved by parametric search, and provide efficient and simple algorithms. Our technique improves the solutions obtained by parametric search by a log n factor. For example, we apply the technique to the two-line-center problem, where we want to find two strips that cover a given set S of n points in the plane, so as to minimize the width of the largest of the two strips.

AB - In this paper we apply the selection and optimization technique of Fredrickson and Johnson to a number of geometric selection and optimization problems, some of which have previously been solved by parametric search, and provide efficient and simple algorithms. Our technique improves the solutions obtained by parametric search by a log n factor. For example, we apply the technique to the two-line-center problem, where we want to find two strips that cover a given set S of n points in the plane, so as to minimize the width of the largest of the two strips.

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Glozman A, Kedem K, Shpitalnik G. On some geometric selection and optimization problems via sorted matrices. In Akl SG, Dehne F, Sack JR, Santoro N, editors, Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings. Springer Verlag. 1995. p. 26-37. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-60220-8_48

On some geometric selection and optimization problems via sorted matrices

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