58 : 2 Rectilinear Link Diameter and Radius in a Rectilinear Polygonal

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 1 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’ 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. © Elena Arseneva, Man-Kwun Chiu, Matias Korman, Aleksandar Markovic, Yoshio Okamoto, Aurélien Ooms, André van Renssen, and Marcel Roeloffzen; licensed under Creative Commons License CC-BY 29th International Symposium on Algorithms and Computation (ISAAC 2018). Editors: Wen-Lian Hsu, Der-Tsai Lee, and Chung-Shou Liao; Article No. 58; pp. 58:1–58:13 Leibniz International Proceedings in Informatics Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl Publishing, Germany 58:2 Rectilinear Link Diameter and Radius in a Rectilinear Polygonal Domain diameter and the radius in O(min(n, n2 + nh log 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 logn) time. 2012 ACM Subject Classification Theory of computation → Computational geometry