On-line partitioning of width w posets into w^O(log log w) chains
share
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.
READ FULL TEXT