@inproceedings{5e963fdf3f7d41599ea28ee8d688b16f,
title = "Rectilinear link diameter and radius in a rectilinear polygonal domain",
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.",
keywords = "Diameter, Polygonal domain, Radius, Rectilinear link distance",
author = "Elena Arseneva and Chiu, {Man Kwun} and Matias Korman and Aleksandar Markovic and Yoshio Okamoto and Aur{\'e}lien Ooms and {Van Renssen}, Andr{\'e} and Marcel Roeloffzen",
note = "Funding Information: Partially supported by the SNF Early Postdoc Mobility grant P2TIP2-168563, Switzerland, and F.R.S.-FNRS, Belgium. 2 Supported in part by ERC StG 757609. 3 Supported in part by KAKENHI No. 17K12635, Japan and NSF award CCF-1422311. 4 Supported by the Netherlands{\textquoteright} Organisation for Scientific Research (NWO) under project no. 024.002.003. 5 Partially supported by JSPS KAKENHI Grant Number 15K00009 and JST CREST Grant Number JPMJCR1402, and Kayamori Foundation of Informational Science Advancement. 6 Supported by the Fund for Research Training in Industry and Agriculture (FRIA). 7 Supported by JST ERATO Grant Number JPMJER1201, Japan. Publisher Copyright: {\textcopyright} Andreas Bj{\"o}rklund;; 29th International Symposium on Algorithms and Computation, ISAAC 2018 ; Conference date: 16-12-2018 Through 19-12-2018",
year = "2018",
month = dec,
day = "1",
doi = "10.4230/LIPIcs.ISAAC.2018.58",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
pages = "58:1--58:13",
editor = "Chung-Shou Liao and Wen-Lian Hsu and Der-Tsai Lee",
booktitle = "29th International Symposium on Algorithms and Computation, ISAAC 2018",
}