An Improved Bound for First-Fit on Posets Without Two Long Incomparable Chains
Combinatorics
2015-03-19 v3
Abstract
It is known that the First-Fit algorithm for partitioning a poset P into chains uses relatively few chains when P does not have two incomparable chains each of size k. In particular, if P has width w then Bosek, Krawczyk, and Szczypka (SIAM J. Discrete Math., 23(4):1992--1999, 2010) proved an upper bound of ckw^{2} on the number of chains used by First-Fit for some constant c, while Joret and Milans (Order, 28(3):455--464, 2011) gave one of ck^{2}w. In this paper we prove an upper bound of the form ckw. This is best possible up to the value of c.
Keywords
Cite
@article{arxiv.1111.2370,
title = {An Improved Bound for First-Fit on Posets Without Two Long Incomparable Chains},
author = {Vida Dujmović and Gwenaël Joret and David R. Wood},
journal= {arXiv preprint arXiv:1111.2370},
year = {2015}
}
Comments
v3: referees' comments incorporated