A refined analysis on the jump number problem of interval orders

• We show that the algorithm for jump number problem have competitive ratio 16/11.
• Our analysis improves the best known ratio 89/60.
• Our approach relies on the refined analysis of Krysztowiak's algorithm.

It is NP-complete to calculate the jump number on an interval order. There are three algorithms reaching 3/2 approximation ratio for this problem. Recently, Krysztowiak improved this ratio to 89/60. We investigate their algorithm carefully and bound this ratio by 16/11.