Rectilinear link diameter and radius in a rectilinear polygonal domain

Elena Arseneva; Man Kwun Chiu; Matias Korman; Aleksandar Markovic; Yoshio Okamoto; Aurélien Ooms; André Van Renssen; Marcel Roeloffzen

doi:10.4230/LIPIcs.ISAAC.2018.58

Rectilinear link diameter and radius in a rectilinear polygonal domain

Elena Arseneva, Man Kwun Chiu, Matias Korman, Aleksandar Markovic, Yoshio Okamoto, Aurélien Ooms, André Van Renssen, Marcel Roeloffzen

INF - System Information Sciences

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

1 Citation (Scopus)

Abstract

We study the computation of the diameter and radius under the rectilinear link distance within a rectilinear polygonal domain of n vertices and h holes. We introduce a graph of oriented distances to encode the distance between pairs of points of the domain. This helps us transform the problem so that we can search through the candidates more efficiently. Our algorithm computes both the diameter and the radius in O(min(n^ω, n² + nhlog h + χ²)) time, where ω < 2.373 denotes the matrix multiplication exponent and χ ∈ Ω(n) ∩ O(n²) is the number of edges of the graph of oriented distances. We also provide an alternative algorithm for computing the diameter that runs in O(n² log n) time.

Original language	English
Title of host publication	29th International Symposium on Algorithms and Computation, ISAAC 2018
Editors	Chung-Shou Liao, Wen-Lian Hsu, Der-Tsai Lee
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages	58:1-58:13
ISBN (Electronic)	9783959770941
DOIs	https://doi.org/10.4230/LIPIcs.ISAAC.2018.58
Publication status	Published - 2018 Dec 1
Event	29th International Symposium on Algorithms and Computation, ISAAC 2018 - Jiaoxi, Yilan, Taiwan, Province of China Duration: 2018 Dec 16 → 2018 Dec 19

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	123
ISSN (Print)	1868-8969

Conference

Conference	29th International Symposium on Algorithms and Computation, ISAAC 2018
Country	Taiwan, Province of China
City	Jiaoxi, Yilan
Period	18/12/16 → 18/12/19

Keywords

Diameter
Polygonal domain
Radius
Rectilinear link distance

ASJC Scopus subject areas

Software

Access to Document

10.4230/LIPIcs.ISAAC.2018.58

Cite this

Arseneva, E., Chiu, M. K., Korman, M., Markovic, A., Okamoto, Y., Ooms, A., Van Renssen, A., & Roeloffzen, M. (2018). Rectilinear link diameter and radius in a rectilinear polygonal domain. In C-S. Liao, W-L. Hsu, & D-T. Lee (Eds.), 29th International Symposium on Algorithms and Computation, ISAAC 2018 (pp. 58:1-58:13). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 123). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ISAAC.2018.58

Rectilinear link diameter and radius in a rectilinear polygonal domain. / Arseneva, Elena; Chiu, Man Kwun; Korman, Matias; Markovic, Aleksandar; Okamoto, Yoshio; Ooms, Aurélien; Van Renssen, André; Roeloffzen, Marcel.

29th International Symposium on Algorithms and Computation, ISAAC 2018. ed. / Chung-Shou Liao; Wen-Lian Hsu; Der-Tsai Lee. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. p. 58:1-58:13 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 123).

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

Arseneva, E, Chiu, MK, Korman, M, Markovic, A, Okamoto, Y, Ooms, A, Van Renssen, A & Roeloffzen, M 2018, Rectilinear link diameter and radius in a rectilinear polygonal domain. in C-S Liao, W-L Hsu & D-T Lee (eds), 29th International Symposium on Algorithms and Computation, ISAAC 2018. Leibniz International Proceedings in Informatics, LIPIcs, vol. 123, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, pp. 58:1-58:13, 29th International Symposium on Algorithms and Computation, ISAAC 2018, Jiaoxi, Yilan, Taiwan, Province of China, 18/12/16. https://doi.org/10.4230/LIPIcs.ISAAC.2018.58

Arseneva E, Chiu MK, Korman M, Markovic A, Okamoto Y, Ooms A et al. Rectilinear link diameter and radius in a rectilinear polygonal domain. In Liao C-S, Hsu W-L, Lee D-T, editors, 29th International Symposium on Algorithms and Computation, ISAAC 2018. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2018. p. 58:1-58:13. (Leibniz International Proceedings in Informatics, LIPIcs). https://doi.org/10.4230/LIPIcs.ISAAC.2018.58

Arseneva, Elena ; Chiu, Man Kwun ; Korman, Matias ; Markovic, Aleksandar ; Okamoto, Yoshio ; Ooms, Aurélien ; Van Renssen, André ; Roeloffzen, Marcel. / Rectilinear link diameter and radius in a rectilinear polygonal domain. 29th International Symposium on Algorithms and Computation, ISAAC 2018. editor / Chung-Shou Liao ; Wen-Lian Hsu ; Der-Tsai Lee. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. pp. 58:1-58:13 (Leibniz International Proceedings in Informatics, LIPIcs).

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abstract = "We study the computation of the diameter and radius under the rectilinear link distance within a rectilinear polygonal domain of n vertices and h holes. We introduce a graph of oriented distances to encode the distance between pairs of points of the domain. This helps us transform the problem so that we can search through the candidates more efficiently. Our algorithm computes both the diameter and the radius in O(min(nω, n2 + nhlog h + χ2)) time, where ω < 2.373 denotes the matrix multiplication exponent and χ ∈ Ω(n) ∩ O(n2) is the number of edges of the graph of oriented distances. We also provide an alternative algorithm for computing the diameter that runs in O(n2 log n) time.",

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AU - Ooms, Aurélien

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N2 - We study the computation of the diameter and radius under the rectilinear link distance within a rectilinear polygonal domain of n vertices and h holes. We introduce a graph of oriented distances to encode the distance between pairs of points of the domain. This helps us transform the problem so that we can search through the candidates more efficiently. Our algorithm computes both the diameter and the radius in O(min(nω, n2 + nhlog h + χ2)) time, where ω < 2.373 denotes the matrix multiplication exponent and χ ∈ Ω(n) ∩ O(n2) is the number of edges of the graph of oriented distances. We also provide an alternative algorithm for computing the diameter that runs in O(n2 log n) time.

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