On the Online Dial-A-Ride Problem with Time-Windows

In this paper the first results on the Online Dial-A-Ride Problem with Time-Windows (ODARPTW for short) are presented. Requests for rides appearing over time consist of two points in a metric space, a source and a destination. Servers transport objects of requests from sources to destinations. Each request specifies a deadline. If a request is not be served by its deadline, it will be called off. The goal is to plan the motion of servers in an online way so that the maximum number of requests is met by their deadlines. We perform competitive analysis of two deterministic strategies for the problem with a single server in two cases separately, where the server has unit capacity and where the server has infinite capacity. The competitive ratios of the strategies are obtained. We also prove a lower bound on the competitive ratio of any deterministic algorithm of $\frac{2-T}{2T}$ for a server with unit capacity and of $\frac{2-T}{2T} \lceil \frac{1}{T} \rceil$ for a server with infinite capacity, where T denotes the diameter of the metric space.

[1]  Rajeev Raman,et al.  Algorithms — ESA 2002 , 2002, Lecture Notes in Computer Science.

[2]  Noga Alon,et al.  A Graph-Theoretic Game and Its Application to the k-Server Problem , 1995, SIAM J. Comput..

[3]  Leen Stougie,et al.  On-Line Dial-a-Ride Problems under a Restricted Information Model , 2002, ESA.

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

[5]  Xu Yin.  Scheduling for on-line taxi problem and competitive algorithm on constrained graphs , 1999 .

[6]  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.

[7]  Sandy Irani,et al.  On-Line Algorithms for the Dynamic Traveling Repair Problem , 2002, SODA '02.

[8]  Yin-Feng Xu,et al.  Online Dial-A-Ride Problem with Time-Windows Under a Restricted Information Model , 2006, AAIM.

[9]  Allan Borodin,et al.  A new measure for the study of on-line algorithms , 2005, Algorithmica.

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

[11]  Wei-Min Ma,et al.  Scheduling for on-line taxi problem on a real line and competitive algorithms , 2004, Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826).

[12]  Klaus Jansen,et al.  Approximation Algorithms for Combinatorial Optimization , 2000 .

[13]  Nicole Megow,et al.  How to Whack Moles , 2003, WAOA.

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

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

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

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

[18]  Yin-Feng Xu,et al.  On-line k-Truck Problem and Its Competitive Algorithms , 2001, J. Glob. Optim..

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

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

[21]  Costas S. Iliopoulos,et al.  A New Efficient Algorithm for Computing the Longest Common Subsequence , 2007, AAIM.