Randomized Online Algorithms for Set Cover Leasing Problems

S. Abshoff, C. Markarian, F. Meyer auf der Heide, in: Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA), 2014, pp. 25–34.

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Abstract
In the leasing variant of Set Cover presented by Anthony et al.[1], elements U arrive over time and must be covered by sets from a familyF of subsets of U. Each set can be leased for K different periods of time.Let |U| = n and |F| = m. Leasing a set S for a period k incurs a cost ckS and allows S to cover its elements for the next lk time steps. The objectiveis to minimize the total cost of the sets leased, such that elements arrivingat any time t are covered by sets which contain them and are leased duringtime t. Anthony et al. [1] gave an optimal O(log n)-approximation forthe problem in the offline setting, unless P = NP [22]. In this paper, wegive randomized algorithms for variants of Set Cover Leasing in the onlinesetting, including a generalization of Online Set Cover with Repetitionspresented by Alon et al. [2], where elements appear multiple times andmust be covered by a different set at each arrival. Our results improve theO(log2(mn)) competitive factor of Online Set Cover with Repetitions [2]to O(log d log(dn)) = O(logmlog(mn)), where d is the maximum numberof sets an element belongs to.
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Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA)
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25-34
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Abshoff S, Markarian C, Meyer auf der Heide F. Randomized Online Algorithms for Set Cover Leasing Problems. In: Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA). LNCS. ; 2014:25-34. doi:10.1007/978-3-319-12691-3_3
Abshoff, S., Markarian, C., & Meyer auf der Heide, F. (2014). Randomized Online Algorithms for Set Cover Leasing Problems. In Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA) (pp. 25–34). https://doi.org/10.1007/978-3-319-12691-3_3
@inproceedings{Abshoff_Markarian_Meyer auf der Heide_2014, series={LNCS}, title={Randomized Online Algorithms for Set Cover Leasing Problems}, DOI={10.1007/978-3-319-12691-3_3}, booktitle={Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA)}, author={Abshoff, Sebastian and Markarian, Christine and Meyer auf der Heide, Friedhelm}, year={2014}, pages={25–34}, collection={LNCS} }
Abshoff, Sebastian, Christine Markarian, and Friedhelm Meyer auf der Heide. “Randomized Online Algorithms for Set Cover Leasing Problems.” In Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA), 25–34. LNCS, 2014. https://doi.org/10.1007/978-3-319-12691-3_3.
S. Abshoff, C. Markarian, and F. Meyer auf der Heide, “Randomized Online Algorithms for Set Cover Leasing Problems,” in Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA), 2014, pp. 25–34.
Abshoff, Sebastian, et al. “Randomized Online Algorithms for Set Cover Leasing Problems.” Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA), 2014, pp. 25–34, doi:10.1007/978-3-319-12691-3_3.
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