Online k-Server Routing Problems

In an online k-server routing problem, a crew of k servers has to visit points in a metric space as they arrive in real time. Possible objective functions include minimizing the makespan (k-Traveling Salesman Problem) and minimizing the average completion time (k-Traveling Repairman Problem). We give competitive algorithms, resource augmentation results and lower bounds for k-server routing problems on several classes of metric spaces. Surprisingly, in some cases the competitive ratio is dramatically better than that of the corresponding single server problem. Namely, we give a 1+O((logk)/k)-competitive algorithm for the k-Traveling Salesman Problem and the k-Traveling Repairman Problem when the underlying metric space is the real line. We also prove that similar results cannot hold for the Euclidean plane.

[1]  Leen Stougie,et al.  The Online-TSP against Fair Adversaries , 2000, CIAC.

[2]  Leen Stougie,et al.  Non-abusiveness Helps: An O(1)-Competitive Algorithm for Minimizing the Maximum Flow Time in the Online Traveling Salesman Problem , 2002, APPROX.

[3]  Satish Rao,et al.  The k-traveling repairman problem , 2003, SODA '03.

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

[5]  Chul E. Kim,et al.  Approximation algorithms for some routing problems , 1976, 17th Annual Symposium on Foundations of Computer Science (sfcs 1976).

[6]  Jirí Sgall,et al.  On-line Scheduling , 1996, Online Algorithms.

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

[8]  Balaji Raghavachari,et al.  Minimum Latency Tours and the k-Traveling Repairmen Problem , 2004, LATIN.

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

[10]  N. Biggs.  THE TRAVELING SALESMAN PROBLEM A Guided Tour of Combinatorial Optimization , 1986 .

[11]  Lyle A. McGeoch,et al.  Competitive Algorithms for Server Problems , 1990, J. Algorithms.

[12]  Sven Oliver Krumke,et al.  The Online Dial-a-Ride Problem under Reasonable Load , 2000, CIAC.

[13]  Leen Stougie,et al.  Randomized algorithms for on-line scheduling problems: how low can't you go? , 2002, Oper. Res. Lett..

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

[15]  V. Bonifaci,et al.  Models and algorithms for online server routing , 2007 .

[16]  Satish Rao,et al.  Paths, trees, and minimum latency tours , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[17]  Allan Borodin,et al.  On Randomization in On-Line Computation , 1999, Inf. Comput..

[18]  Bala Kalyanasundaram,et al.  Speed is as powerful as clairvoyance , 2000, JACM.

[19]  Bo Chen,et al.  Scheduling on identical machines: How good is LPT in an on-line setting? , 1997, Oper. Res. Lett..

[20]  Leen Stougie,et al.  Non-abusiveness Helps: An % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC% vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbuLwBLnhiov2DGi1BTfMBaeHb% d9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb% L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe% pae9pg0FirpepeKkFr0xfr-xfr , 2002 .

[21]  Leen Stougie,et al.  On-Line Dial-a-Ride Problems Under a Restricted Information Model , 2004, Algorithmica.

[22]  M Maarten Lipmann,et al.  On-line routing , 2003 .

[23]  Allan Borodin,et al.  On randomization in online computation , 1997, Proceedings of Computational Complexity. Twelfth Annual IEEE Conference.

[24]  Leen Stougie,et al.  News from the online traveling repairman , 2003, Theor. Comput. Sci..

[25]  Giorgio Ausiello,et al.  The On-line Asymmetric Traveling Salesman Problem , 2005, WADS.