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

Authors Alexander Birx, Yann Disser, Kevin Schewior

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Alexander Birx
  • Institute of Mathematics and Graduate School CE, TU Darmstadt, Germany
Yann Disser
  • Institute of Mathematics, TU Darmstadt, Germany
Kevin Schewior
  • Institut für Informatik, Technische Universität München, Garching, Germany

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Alexander Birx, Yann Disser, and Kevin Schewior. Improved Bounds for Open Online Dial-a-Ride on the Line. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Mathematics of computing → Combinatorial optimization
  • dial-a-ride on the line
  • elevator problem
  • online algorithms
  • competitive analysis
  • smartstart
  • competitive ratio


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