A QPTAS for the base of the number of crossing-free structures on a planar point set

Research output: Contribution to journalArticle

Abstract

The number of triangulations of a planar n point set S is known to be cn, where the base c lies between 2.43 and 30. Similarly, the number of crossing-free spanning trees on S is known to be dn, where the base d lies between 6.75 and 141.07. The fastest known algorithm for counting triangulations of S runs in 2(1+o(1))nlog n time while that for counting crossing-free spanning trees runs in O (7.125n) time. The fastest known, non-trivial approximation algorithms for the number of triangulations of S and the number of crossing-free spanning trees of S, respectively, run in time subexponential in n. We present the first non-trivial approximation algorithms for these numbers running in quasi-polynomial time. They yield the first quasi-polynomial approximation schemes for the base of the number of triangulations of S and the base of the number of crossing-free spanning trees on S, respectively.

Details

Authors
Organisations
External organisations
  • University of Bonn
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Computer Science

Keywords

  • Approximation algorithms, Computational geometry, Counting spanning trees, Counting triangulations, Quasi-polynomial-time approximation scheme
Original languageEnglish
Pages (from-to)56-65
JournalTheoretical Computer Science
Volume711
Early online date2017 Nov 16
Publication statusPublished - 2018 Feb
Publication categoryResearch
Peer-reviewedYes