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. Feuerstein and Stougie [8] present a 9-competitive algorithm for the OlTrp on the real line. In this paper we show how to use techniques from online-scheduling to obtain a 6-competitive deterministic algorithm for the OlTrp on any metric space. We also present a randomized algorithm with competitive ratio of 3/ln 2 2.1282 for the L-OLDARP on the line, 4e-5/2e-3 > 2.41041 for the L-OLDARP on general metric spaces, 2 for the OLTRP on the line, and 7/3 for the OLTRP on general metric spaces.

[1]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[2]  Jon M. Kleinberg,et al.  An improved approximation ratio for the minimum latency problem , 1996, SODA '96.

[3]  David B. Shmoys,et al.  Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms , 1997, Math. Oper. Res..

[4]  Sanjeev Arora,et al.  Approximation schemes for minimum latency problems , 1999, STOC '99.

[5]  Leen Stougie,et al.  Algorithms for the On-Line Travelling Salesman1 , 2001, Algorithmica.

[6]  Sven Oliver Krumke,et al.  Online Dial-a-Ride Problems: Minimizing the Completion Time , 2000, STACS.

[7]  Steven S. Seiden,et al.  A guessing game and randomized online algorithms , 2000, STOC '00.

[8]  David B. Shmoys,et al.  Scheduling to minimize average completion time: off-line and on-line algorithms , 1996, SODA '96.

[9]  WeinJoel,et al.  Scheduling to Minimize Average Completion Time , 1997 .

[10]  Leen Stougie,et al.  On-line single-server dial-a-ride problems , 2001, Theor. Comput. Sci..

[11]  Leen Stougie,et al.  Competitive Algorithms for the On-line Traveling Salesman , 1995, WADS.

[12]  Cynthia A. Phillips,et al.  Improved Scheduling Algorithms for Minsum Criteria , 1996, ICALP.

[13]  Russ Bubley,et al.  Randomized algorithms , 2018, CSUR.

[14]  George Papageorgiou,et al.  The Complexity of the Travelling Repairman Problem , 1986, RAIRO Theor. Informatics Appl..

[15]  Madhu Sudan,et al.  The minimum latency problem , 1994, STOC '94.