Improved approximation algorithm for the jump number of interval orders

The jump number problem for posets is to find a linear extension in which the number of incomparable adjacent pairs is minimized. In this paper the class of interval orders is considered. Three 3/2-approximation algorithms for this problem have been known for some time. By a previous work of Mitas, the problem may be reformulated as a subgraph packing task. We prove that the problem reduces also to a set cover task, and we establish an improved bound of 1.484 to the approximation ratio of the jump number on interval orders.