Bipartite diameter and other measures under translation

Boris Aronov, Omrit Filtser, Matthew J. Katz, Khadijeh Sheikhan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Let A and B be two sets of points in Rd, where |A| = |B| = n and the distance between them is defined by some bipartite measure dist(A, B). We study several problems in which the goal is to translate the set B, so that dist(A, B) is minimized. The main measures that we consider are (i) the diameter in two and three dimensions, that is diam(A, B) = max{d(a, b) | a ∈ A, b ∈ B}, where d(a, b) is the Euclidean distance between a and b, (ii) the uniformity in the plane, that is uni(A, B) = diam(A, B) − d(A, B), where d(A, B) = min{d(a, b) | a ∈ A, b ∈ B}, and (iii) the union width in two and three dimensions, that is union_width(A, B) = width(A ∪ B).

Original languageEnglish
Title of host publication36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019
EditorsRolf Niedermeier, Christophe Paul
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771009
DOIs
StatePublished - 1 Mar 2019
Externally publishedYes
Event36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019 - Berlin, Germany
Duration: 13 Mar 201916 Mar 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume126
ISSN (Print)1868-8969

Conference

Conference36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019
Country/TerritoryGermany
CityBerlin
Period13/03/1916/03/19

Bibliographical note

Publisher Copyright:
© Boris Aronov, Omrit Filtser, Matthew J. Katz, and Khadijeh Sheikhan.

Keywords

  • Geometric optimization
  • Minimum-width annulus
  • Translation-invariant similarity measures

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