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Tight Analysis of the Smartstart Algorithm for Online Dial-a-Ride on the Line

Authors Alexander Birx, Yann Disser



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LIPIcs.STACS.2019.15.pdf
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Alexander Birx
  • Institute of Mathematics and Graduate School CE, TU Darmstadt, Germany
Yann Disser
  • Institute of Mathematics and Graduate School CE, TU Darmstadt, Germany

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Alexander Birx and Yann Disser. Tight Analysis of the Smartstart Algorithm for Online Dial-a-Ride on the Line. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 15:1-15:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.STACS.2019.15

Abstract

The online Dial-a-Ride problem is a fundamental online problem in a metric space, where transportation requests appear over time and may be served in any order by a single server with unit speed. Restricted to the real line, online Dial-a-Ride captures natural problems like controlling a personal elevator. Tight results in terms of competitive ratios are known for the general setting and for online TSP on the line (where source and target of each request coincide). In contrast, online Dial-a-Ride on the line has resisted tight analysis so far, even though it is a very natural online problem. We conduct a tight competitive analysis of the Smartstart algorithm that gave the best known results for the general, metric case. In particular, our analysis yields a new upper bound of 2.94 for open, non-preemptive online Dial-a-Ride on the line, which improves the previous bound of 3.41 [Krumke'00]. The best known lower bound remains 2.04 [SODA'17]. We also show that the known upper bound of 2 [STACS'00] regarding Smartstart’s competitive ratio for closed, non-preemptive online Dial-a-Ride is tight on the line.

Subject Classification

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

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References

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