News from the online traveling repairman

In the traveling repairman problem (Trp), a tour must be found through every one of a set of points (cities) in some metric space such that the weighted sum of completion times of the cities is minimized. Given a tour, the completion time of a city is the time traveled on the tour before the city is reached. In the online traveling repairman problem (OLTrp) requests for visits to cities arrive online while the repairman is traveling. We analyze the performance of algorithms for the online problem using competitive analysis, where the cost of an online algorithm is compared to that of an optimal offline algorithm. We show how to use techniques from online-scheduling to obtain a deterministic algorithm with a competitive ratio of (1+2)22.41041 for the L-OlDarp on general metric spaces, 2 for the OlTrp on the line, and 73 for the OlTrp on general metric spaces.