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arXiv · 1111.2370

An Improved Bound for First-Fit on Posets Without Two Long Incomparable Chains

Vida Dujmović·Gwenaël Joret·David R. Wood
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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.

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Vida Dujmović, Gwenaël Joret, David R. Wood. 2012-06-15. An Improved Bound for First-Fit on Posets Without Two Long Incomparable Chains. https://doi.org/10.1137/110855806

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