On-line partitioning of width w posets into w^O(log log w) chains

09/29/2018

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by   Bartłomiej Bosek, et al.

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An on-line chain partitioning algorithm receives the vertices of a poset one at a time, and when a vertex is received, irrevocably assigns it to one of the chains. In this paper we present an on-line algorithm that partitions posets of width w into w^O(w) chains. This improves over previously best known algorithms using w^O(w) chains by Bosek and Krawczyk and by Bosek, Kierstead, Krawczyk, Matecki, and Smith.