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On the Bahncard Problem

  • Rudolf Fleischer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1449)

Abstract

In this paper, we generalize the Ski-Rental Problem to the Bahncard Problem which is an online problem of practical relevance for all travelers. The Bahncard is a railway pass of the Deutsche Bundesbahn (the German railway company) which entitles its holder to a 50% price reduction on nearly all train tickets. It costs 240DM, and it is valid for 12 months. Similar bus or railway passes can be found in many other countries.

For the common traveler, the decision at which time to buy a Bahncard is a typical online problem, because she usually does not know when and to which place she will travel next. We show that the greedy algorithm applied by most travelers and clerks at ticket offices is not better in the worst case than the trivial algorithm which never buys a Bahncard. We present two optimal deterministic online algorithms, an optimistic one and and a pessimistic one. We further give a lower bound for randomized online algorithms and present an algorithm which we conjecture to be optimal; a proof of the conjecture is given for a special case of the problem.

Keywords

Competitive Ratio Online Algorithm Springer Lecture Note Ticket Price Request Sequence 
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 1998

Authors and Affiliations

  • Rudolf Fleischer
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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