A fast 4-approximation algorithm for the traveling repairman problem on a line

The traveling repairman problem is a scheduling problem in which a repairman is supposed to visit some customers at their locations to perform some jobs. Each customer has a time window during which the repairman is allowed to arrive to perform the jobs. The goal is to maximize the number of visited locations. In this work we deal with a special case in which the locations are on a line, the processing time of each job is zero, and the time window length is unitary. Although the general TRP is NP-Hard, the complexity of this special case remains unknown. We introduce a quadratic 4-approximation algorithm based on the 8-approximation algorithm proposed in 2005 by R. Bar-Yehuda, G. Even, and S. Shahar.