Ham-Sandwich Cuts for Abstract Order Types

Stefan Felsner, Alexander Pilz

Research output: Contribution to journalArticleResearchpeer-review

Abstract

The linear-time ham-sandwich cut algorithm of Lo, Matoušek, and Steiger for bi-chromatic finite point sets in the plane works by appropriately selecting crossings of the lines in the dual line arrangement with a set of well-chosen vertical lines. We consider the setting where we are not given the coordinates of the point set, but only the orientation of each point triple (the order type) and give a deterministic linear-time algorithm for the mentioned sub-algorithm. This yields a linear-time ham-sandwich cut algorithm even in our restricted setting. We also show that our methods are applicable to abstract order types.

Original languageEnglish
Pages (from-to)234-257
Number of pages24
JournalAlgorithmica
Volume80
Issue number1
DOIs
Publication statusPublished - 1 Jan 2018
Externally publishedYes

Fingerprint

Order Type
Sandwich
Point Sets
Linear Time
Line
Triple Point
Deterministic Algorithm
Linear-time Algorithm
Finite Set
Arrangement
Vertical

Keywords

  • Abstract order type
  • Ham-sandwich cut
  • Pseudo-line arrangement

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

Cite this

Ham-Sandwich Cuts for Abstract Order Types. / Felsner, Stefan; Pilz, Alexander.

In: Algorithmica, Vol. 80, No. 1, 01.01.2018, p. 234-257.

Research output: Contribution to journalArticleResearchpeer-review

Felsner, Stefan ; Pilz, Alexander. / Ham-Sandwich Cuts for Abstract Order Types. In: Algorithmica. 2018 ; Vol. 80, No. 1. pp. 234-257.
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