Abstract
We consider deterministic online algorithms for paging. The offline version of the paging problem, in which the whole input is given in advance, is known to be easily solvable. If the input is random, chosen according to some known probability distribution, an \(\mathcal {O}\mathopen {}\left( \log k\right) \)-competitive algorithm exists. Moreover, there are distributions, where no algorithm can be better than \(\mathrm {\Omega }\mathopen {}\left( \log k\right) \)-competitive.
In this paper, we ask the question of what happens if it is known that the input is one from a set of \(\ell \) potential candidates, chosen according to some probability distribution. We present an \(\mathcal {O}\mathopen {}\left( \log \ell \right) \)-competitive algorithm, and show a matching lower bound.
The research is partially funded by SNF grant 200021–146372, VEGA grant 1/0979/12, and Deutsche Forschungsgemeinschaft grant BL511/10-1.
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Notes
- 1.
Note that unlike offline algorithms, in an online setting we usually ignore the running time of the algorithm.
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Acknowledgement
The authors would like to thank Hans-Joachim Böckenhauer for very valuable discussions.
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Dobrev, S., Hromkovič, J., Komm, D., Královič, R., Královič, R., Mömke, T. (2016). The Complexity of Paging Against a Probabilistic Adversary. In: Freivalds, R., Engels, G., Catania, B. (eds) SOFSEM 2016: Theory and Practice of Computer Science. SOFSEM 2016. Lecture Notes in Computer Science(), vol 9587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49192-8_22
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