On first-fit coloring of ladder-free posets

Henry Kierstead, Matt Earl Smith

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Bosek and Krawczyk exhibited an on-line algorithm for partitioning an on-line poset of width w into w14lgw chains. They also observed that the problem of on-line chain partitioning of general posets of width w could be reduced to First-Fit chain partitioning of 2w 2+1-ladder-free posets of width w, where an m-ladder is the transitive closure of the union of two incomparable chains x 1 ≤ ⋯ ≤ x m, y 1 ≤ ⋯ ≤ y m and the set of comparabilities Zx 1 ≤ y 1, x m ≤ y m } Here, we provide a subexponential upper bound (in terms of w with m fixed) for the performance of First-Fit chain partitioning on m-ladder-free posets, as well as an exact quadratic bound when m = 2, and an upper bound linear in m when w=2. Using the Bosek-Krawczyk observation, this yields an on-line chain partitioning algorithm with a somewhat improved performance bound. More importantly, the algorithm and the proof of its performance bound are much simpler.

Original languageEnglish (US)
Pages (from-to)474-489
Number of pages16
JournalEuropean Journal of Combinatorics
Volume34
Issue number2
DOIs
StatePublished - Feb 2013

Fingerprint

Ladders
Coloring
Poset
Colouring
Partitioning
Performance Bounds
Upper bound
Transitive Closure
Union

ASJC Scopus subject areas

  • Geometry and Topology
  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

On first-fit coloring of ladder-free posets. / Kierstead, Henry; Smith, Matt Earl.

In: European Journal of Combinatorics, Vol. 34, No. 2, 02.2013, p. 474-489.

Research output: Contribution to journalArticle

Kierstead, Henry ; Smith, Matt Earl. / On first-fit coloring of ladder-free posets. In: European Journal of Combinatorics. 2013 ; Vol. 34, No. 2. pp. 474-489.
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