On-line Chain Partitioning of Up-growing Interval Orders

On-line chain partitioning problem of on-line posets has been open for the past 20 years. The best known on-line algorithm uses 5w −1 4 chains to cover poset of width w. Felsner [3] introduced a variant of this problem considering only up-growing posets, i.e. on-line posets in which each new point is maximal at the moment of its arrival. He presented an algorithm using w+1 2 chains for width w posets and proved that his solution is optimal. In this paper, we study on-line chain partitioning of up-growing interval orders. We prove lower bound and upper bound to be 2w − 1 for width w posets.

• Type: Journal
• Year: 2007
• Where: ORDER
• Authors: Patrick Baier, Bartlomiej Bosek, Piotr Micek
• Keywords: Chain, On-line, On-line Posets, ORDER 2007