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
Journal of Algorithms
Competitive randomized algorithms for non-uniform problems
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
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
Dynamic TCP acknowledgement and other stories about e/(e-1)
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Average-Case Competitive Analyses for Ski-Rental Problems
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
On the remote server problem or more about TCP acknowledgments
Theoretical Computer Science
Dynamic TCP acknowledgment with sliding window
Theoretical Computer Science
On the on-line k-taxi problem with limited look ahead
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Competitive analysis of two special online device replacement problems
Journal of Computer Science and Technology
The ski-rental problem with multiple discount options
Information Processing Letters
Algorithms for optimizing the bandwidth cost of content delivery
Computer Networks: The International Journal of Computer and Telecommunications Networking
On the best possible competitive ratio for multislope ski rental
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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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. 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 where 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 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. It turns out that the optimal competitive ratio only depends on the price reduction factor (50% for the German Bahncard Problem), but does not depend on the price or validity period of a Bahncard. Copyright 2001 Elsevier Science B.V.