Maximin location of convex objects in a polygon and related dynamic voronoi diagrams

Hiromi Aonuma, Hiroshi Imai, Keiko Imai, Takeshi Tokuyama

Research output: Chapter in Book/Report/Conference proceedingConference contribution

16 Citations (Scopus)

Abstract

This paper considers the maximin placement of a convex polygon P inside a polygon Q, and introduce several new static and dynamic Voronoi diagrams to solve the problem. It is shown that P can be placed inside Q, using translation and rotation, so that the minimum Euclidean distance between any point on P and any point on Q is maximized in O(m416(mn)log mn) time, where m and n are the numbers of edges of P and Q, respectively, and λ16(N) is the maximum length of Davenport-Schinzel sequences on N alphabets of order 16. If only translation is allowed, the problem can be solved in O(mn log mn) time. The problem of placing multiple translates of P inside Q in a maximin manner is also considered, and in connection with this problem the dynamic Voronoi diagram of k rigidly moving sets of n points is investigated. The combinatorial complexity of this canonical dynamic diagram for kn points is shown to be O(n2) and O(n3k4 log* k) for k = 2,3 and k ≥ 4, respectively. Several related problems are also treated in a unified way.

Original languageEnglish
Title of host publicationProc Sixth Annu Symp Comput Geom
PublisherPubl by ACM
Pages225-234
Number of pages10
ISBN (Print)0897913620, 9780897913621
DOIs
Publication statusPublished - 1990
EventProceedings of the Sixth Annual Symposium on Computational Geometry - Berkeley, CA, USA
Duration: 1990 Jun 61990 Jun 8

Publication series

NameProc Sixth Annu Symp Comput Geom

Conference

ConferenceProceedings of the Sixth Annual Symposium on Computational Geometry
CityBerkeley, CA, USA
Period90/6/690/6/8

ASJC Scopus subject areas

  • Engineering(all)

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