First-Fit Algorithm for the On-Line Chain Partitioning Problem

  • Authors:

  • BartŁomiej Bosek;Tomasz Krawczyk;Edward Szczypka

  • Affiliations:

  • bosek@tcs.uj.edu.pl and krawczyk@tcs.uj.edu.pl and szczypka@tcs.uj.edu.pl;-;-

  • Venue:
  • SIAM Journal on Discrete Mathematics
  • Year:
  • 2010

Quantified Score

Hi-index 0.00

Visualization

Abstract

We consider a problem of partitioning a partially ordered set into chains by first-fit algorithm. In general this algorithm uses arbitrarily many chains on a class of bounded width posets. In this paper we prove that First-Fit uses at most $3tw^2$ chains to partition any poset of width $w$ which does not induce two incomparable chains of height $t$. In this way we get a wide class of posets with polynomial bound for the on-line chain partitioning problem. We also discuss some consequences of our result for coloring graphs by First-Fit.