An Easy Subexponential Bound for Online Chain Partitioning

  • Bartłomiej Bosek
  • H. A. Kierstead
  • Tomasz Krawczyk
  • Grzegorz Matecki
  • Matthew E. Smith
DOI: https://doi.org/10.37236/7231
Keywords: Partially ordered set, Poset, First-fit, Online chain partition, Ladder, Regular poset

Abstract

Bosek and Krawczyk exhibited an online algorithm for partitioning an online poset of width $w$ into $w^{14\lg w}$ chains. We improve this to $w^{6.5 \lg w + 7}$ with a simpler and shorter proof by combining the work of Bosek & Krawczyk with work of Kierstead & Smith on First-Fit chain partitioning of ladder-free posets. We also provide examples illustrating the limits of our approach.

Author Biographies

Bartłomiej Bosek, Jagiellonian University in Kraków

Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian Univesity in Kraków

H. A. Kierstead, Arizona State University
School of Mathematical Sciences and Statistics, Arizona State University
Tomasz Krawczyk, Jagiellonian University in Kraków
Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian Univesity in Kraków
Grzegorz Matecki, Jagiellonian University in Kraków
Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian Univesity in Kraków
Matthew E. Smith, Arizona State University
School of Mathematical Sciences and Statistics, Arizona State University
Published
2018-05-25
Issue
Volume 25, Issue 2 (2018)
Article Number
P2.28