The k-Resource Problem on Uniform and on Uniformly Decomposable Metric Spaces

M. Bienkowski, J. Kutyłowski, in: Lecture Notes in Computer Science, Berlin, Heidelberg, 2007.

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We define a natural generalization of the prominent k-server problem, the k-resource problem. It occurs in metric spaces with some demands and resources given at its points. The demands may vary with time, but the total demand may never exceed k. The goal of an online algorithm is to satisfy demands by moving resources, while minimizing the cost for transporting resources. We give an asymptotically optimal O(log(min {n,k}))-competitive randomized algorithm and an O(min {k,n})-competitive deterministic one for the k-resource problem on uniform metric spaces consisting of n points. This extends known results for paging to the more general setting of k-resource. Basing on the results for uniform metric spaces, we develop a randomized algorithm solving the k-resource and the k-server problem on metric spaces which can be decomposed into components far away from each other. The algorithm achieves a competitive ratio of O(log(min {n,k})), provided that it has some extra resources more than the optimal algorithm.
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Bienkowski M, Kutyłowski J. The k-Resource Problem on Uniform and on Uniformly Decomposable Metric Spaces. In: Lecture Notes in Computer Science. ; 2007. doi:10.1007/978-3-540-73951-7_30
Bienkowski, M., & Kutyłowski, J. (2007). The k-Resource Problem on Uniform and on Uniformly Decomposable Metric Spaces. Lecture Notes in Computer Science. https://doi.org/10.1007/978-3-540-73951-7_30
@inproceedings{Bienkowski_Kutyłowski_2007, place={Berlin, Heidelberg}, title={The k-Resource Problem on Uniform and on Uniformly Decomposable Metric Spaces}, DOI={10.1007/978-3-540-73951-7_30}, booktitle={Lecture Notes in Computer Science}, author={Bienkowski, Marcin and Kutyłowski, Jarosław}, year={2007} }
Bienkowski, Marcin, and Jarosław Kutyłowski. “The K-Resource Problem on Uniform and on Uniformly Decomposable Metric Spaces.” In Lecture Notes in Computer Science. Berlin, Heidelberg, 2007. https://doi.org/10.1007/978-3-540-73951-7_30.
M. Bienkowski and J. Kutyłowski, “The k-Resource Problem on Uniform and on Uniformly Decomposable Metric Spaces,” 2007, doi: 10.1007/978-3-540-73951-7_30.
Bienkowski, Marcin, and Jarosław Kutyłowski. “The K-Resource Problem on Uniform and on Uniformly Decomposable Metric Spaces.” Lecture Notes in Computer Science, 2007, doi:10.1007/978-3-540-73951-7_30.

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