Improved Bounds for Open Online Dial-a-Ride on the Line

We consider the open, non-preemptive online Dial-a-Ride problem on the real line, where transportation requests appear over time and need to be served by a single server. We give a lower bound of 2.0585 on the competitive ratio, which is the first bound that strictly separates online Dial-a-Ride on the line from online TSP on the line in terms of competitive analysis, and is the best currently known lower bound even for general metric spaces. On the other hand, we present an algorithm that improves the best known upper bound from 2.9377 to 2.6662. The analysis of our algorithm is tight.

[1]  Lei Tian,et al.  On the Online Dial-A-Ride Problem with Time-Windows , 2005, AAIM.

[2]  Leen Stougie,et al.  Tight Bounds for Online TSP on the Line , 2017, SODA.

[3]  Mikhail J. Atallah,et al.  Efficient Solutions to Some Transportation Problems with Applications to Minimizing Robot Arm Travel , 1988, SIAM J. Comput..

[4]  R. Gomory,et al.  Sequencing a One State-Variable Machine: A Solvable Case of the Traveling Salesman Problem , 1964 .

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

[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]  Sven O. Krumke,et al.  Online Optimization: Competitive Analysis and Beyond , 2002 .

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

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

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

[11]  Dih Jiun Guan,et al.  Routing a Vehicle of Capacity Greater than one , 1998, Discret. Appl. Math..

[12]  Jan Karel Lenstra,et al.  Computer-Aided Complexity Classification of Dial-a-Ride Problems , 2004, INFORMS J. Comput..

[13]  Moses Charikar,et al.  The finite capacity dial-a-ride problem , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

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

[15]  Athanasios Lois,et al.  On the Online Dial-a-Ride Problem , 2016 .

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

[17]  Patrick Jaillet,et al.  Generalized Online Routing: New Competitive Ratios, Resource Augmentation, and Asymptotic Analyses , 2008, Oper. Res..

[18]  Yann Disser,et al.  Tight Analysis of the Smartstart Algorithm for Online Dial-a-Ride on the Line , 2019, STACS.

[19]  Leen Stougie,et al.  On Minimizing the Maximum Flow Time in the Online Dial-a-Ride Problem , 2005, WAOA.

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