Amortized efficiency of list update and paging rules
Communications of the ACM
Data structures and network algorithms
Data structures and network algorithms
New On-Line Algorithms for the Page Replication Problem
SWAT '94 Proceedings of the 4th Scandinavian Workshop on Algorithm Theory
Memory Versus Randomization in On-line Algorithms (Extended Abstract)
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
On-Line Distributed Data Management
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
The bahncard problem with interest rate and risk
WINE'05 Proceedings of the First international conference on Internet and Network Economics
A risk-reward competitive analysis of the bahncard problem
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
Price fluctuations: to buy or to rent
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
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In this paper, we generalize the Ski-Rental Problem to the Bahncard Problem which is an online problem of practical relevance for all travelers.T he 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.I t costs 240DM, and it is valid for 12 months.Si milar 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.W e 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.W e present two optimal deterministic online algorithms, an optimistic one and and a pessimistic one.W e 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.