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The Relative Worst Order Ratio Applied to Seat Reservation

  • Joan Boyar
  • Paul Medvedev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3111)

Abstract

The relative worst order ratio is a new measure for the quality of on-line algorithms, which has been giving new separations and even new algorithms for a variety of problems. Here, we apply the relative worst order ratio to the seat reservation problem, the problem of assigning seats to passengers in a train. For the unit price problem, where all tickets have the same cost, we show that First-Fit and Best-Fit are better than Worst-Fit, even though they have not been separated using the competitive ratio. The same relative worst order ratio result holds for the proportional price problem, where the ticket price is proportional to the distance travelled. In contrast, no deterministic algorithm has a competitive ratio, or even a competitive ratio on accommodating sequences, which is bounded below by a constant. It is also shown that the worst order ratio for seat reservation algorithms is very closely related to the competitive ratio on accommodating sequences.

Keywords

Competitive Ratio Price Policy Interval Graph Deterministic Algorithm Price Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Joan Boyar
    • 1
  • Paul Medvedev
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdenseDenmark

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