Piercing Diametral Disks Induced by Edges of Maximum Spanning Trees

A. Karim Abu-Affash; Paz Carmi; Meytal Maman

doi:10.1007/978-3-031-27051-2_7

Piercing Diametral Disks Induced by Edges of Maximum Spanning Trees

A. Karim Abu-Affash
, Paz Carmi
, Meytal Maman

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

1 Scopus citations

Abstract

Let P be a set of points in the plane and let T be a maximum-weight spanning tree of P. For an edge (p, q), let be the diametral disk induced by (p, q), i.e., the disk having the segment as its diameter. Let be the set of the diametral disks induced by the edges of T. In this paper, we show that one point is sufficient to pierce all the disks in, thus, the set is Helly. Actually, we show that the center of the smallest enclosing circle of P is contained in all the disks of, and thus the piercing point can be computed in linear time.

Original language	English
Title of host publication	WALCOM
Subtitle of host publication	Algorithms and Computation - 17th International Conference and Workshops, WALCOM 2023, Proceedings
Editors	Chun-Cheng Lin, Bertrand M. Lin, Giuseppe Liotta
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	71-77
Number of pages	7
ISBN (Print)	9783031270505
DOIs	https://doi.org/10.1007/978-3-031-27051-2_7
State	Published - 1 Jan 2023
Event	17th International Conference and Workshops on Algorithms and Computation, WALCOM 2023 - Hsinchu, Taiwan, Province of China Duration: 22 Mar 2023 → 24 Mar 2023

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13973 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	17th International Conference and Workshops on Algorithms and Computation, WALCOM 2023
Country/Territory	Taiwan, Province of China
City	Hsinchu
Period	22/03/23 → 24/03/23

Keywords

Fingerhut’s conjecture
Helly’s theorem
Maximum spanning tree
Piercing set

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-031-27051-2_7

Cite this

Abu-Affash, A. K., Carmi, P., & Maman, M. (2023). Piercing Diametral Disks Induced by Edges of Maximum Spanning Trees. In C.-C. Lin, B. M. Lin, & G. Liotta (Eds.), WALCOM: Algorithms and Computation - 17th International Conference and Workshops, WALCOM 2023, Proceedings (pp. 71-77). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13973 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-27051-2_7

Abu-Affash, A. Karim ; Carmi, Paz ; Maman, Meytal. / Piercing Diametral Disks Induced by Edges of Maximum Spanning Trees. WALCOM: Algorithms and Computation - 17th International Conference and Workshops, WALCOM 2023, Proceedings. editor / Chun-Cheng Lin ; Bertrand M. Lin ; Giuseppe Liotta. Springer Science and Business Media Deutschland GmbH, 2023. pp. 71-77 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Let P be a set of points in the plane and let T be a maximum-weight spanning tree of P. For an edge (p, q), let be the diametral disk induced by (p, q), i.e., the disk having the segment as its diameter. Let be the set of the diametral disks induced by the edges of T. In this paper, we show that one point is sufficient to pierce all the disks in, thus, the set is Helly. Actually, we show that the center of the smallest enclosing circle of P is contained in all the disks of, and thus the piercing point can be computed in linear time.",

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Abu-Affash, AK, Carmi, P & Maman, M 2023, Piercing Diametral Disks Induced by Edges of Maximum Spanning Trees. in C-C Lin, BM Lin & G Liotta (eds), WALCOM: Algorithms and Computation - 17th International Conference and Workshops, WALCOM 2023, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13973 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 71-77, 17th International Conference and Workshops on Algorithms and Computation, WALCOM 2023, Hsinchu, Taiwan, Province of China, 22/03/23. https://doi.org/10.1007/978-3-031-27051-2_7

Piercing Diametral Disks Induced by Edges of Maximum Spanning Trees. / Abu-Affash, A. Karim; Carmi, Paz; Maman, Meytal.
WALCOM: Algorithms and Computation - 17th International Conference and Workshops, WALCOM 2023, Proceedings. ed. / Chun-Cheng Lin; Bertrand M. Lin; Giuseppe Liotta. Springer Science and Business Media Deutschland GmbH, 2023. p. 71-77 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13973 LNCS).

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

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AB - Let P be a set of points in the plane and let T be a maximum-weight spanning tree of P. For an edge (p, q), let be the diametral disk induced by (p, q), i.e., the disk having the segment as its diameter. Let be the set of the diametral disks induced by the edges of T. In this paper, we show that one point is sufficient to pierce all the disks in, thus, the set is Helly. Actually, we show that the center of the smallest enclosing circle of P is contained in all the disks of, and thus the piercing point can be computed in linear time.

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Abu-Affash AK, Carmi P, Maman M. Piercing Diametral Disks Induced by Edges of Maximum Spanning Trees. In Lin CC, Lin BM, Liotta G, editors, WALCOM: Algorithms and Computation - 17th International Conference and Workshops, WALCOM 2023, Proceedings. Springer Science and Business Media Deutschland GmbH. 2023. p. 71-77. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-27051-2_7