[{"date_updated":"2022-01-06T06:59:36Z","author":[{"first_name":"Sebastian","last_name":"Abshoff","full_name":"Abshoff, Sebastian"},{"last_name":"Markarian","first_name":"Christine","full_name":"Markarian, Christine","id":"37612"},{"id":"15523","last_name":"Meyer auf der Heide","first_name":"Friedhelm","full_name":"Meyer auf der Heide, Friedhelm"}],"year":"2014","title":"Randomized Online Algorithms for Set Cover Leasing Problems","doi":"10.1007/978-3-319-12691-3_3","series_title":"LNCS","abstract":[{"text":"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.","lang":"eng"}],"publication":"Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA)","department":[{"_id":"63"}],"type":"conference","date_created":"2017-10-17T12:42:06Z","file":[{"date_created":"2018-03-20T07:12:57Z","creator":"florida","file_id":"1395","success":1,"content_type":"application/pdf","file_name":"379-COCOA14.pdf","file_size":214299,"access_level":"closed","relation":"main_file","date_updated":"2018-03-20T07:12:57Z"}],"has_accepted_license":"1","status":"public","user_id":"15504","ddc":["040"],"_id":"379","page":"25-34","project":[{"_id":"1","name":"SFB 901"},{"_id":"5","name":"SFB 901 - Subprojekt A1"},{"_id":"2","name":"SFB 901 - Project Area A"}],"citation":{"chicago":"Abshoff, Sebastian, Christine Markarian, and Friedhelm Meyer auf der Heide. “Randomized Online Algorithms for Set Cover Leasing Problems.” In <i>Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA)</i>, 25–34. LNCS, 2014. <a href=\"https://doi.org/10.1007/978-3-319-12691-3_3\">https://doi.org/10.1007/978-3-319-12691-3_3</a>.","short":"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.","ieee":"S. Abshoff, C. Markarian, and F. Meyer auf der Heide, “Randomized Online Algorithms for Set Cover Leasing Problems,” in <i>Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA)</i>, 2014, pp. 25–34.","apa":"Abshoff, S., Markarian, C., &#38; Meyer auf der Heide, F. (2014). Randomized Online Algorithms for Set Cover Leasing Problems. In <i>Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA)</i> (pp. 25–34). <a href=\"https://doi.org/10.1007/978-3-319-12691-3_3\">https://doi.org/10.1007/978-3-319-12691-3_3</a>","bibtex":"@inproceedings{Abshoff_Markarian_Meyer auf der Heide_2014, series={LNCS}, title={Randomized Online Algorithms for Set Cover Leasing Problems}, DOI={<a href=\"https://doi.org/10.1007/978-3-319-12691-3_3\">10.1007/978-3-319-12691-3_3</a>}, 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} }","ama":"Abshoff S, Markarian C, Meyer auf der Heide F. Randomized Online Algorithms for Set Cover Leasing Problems. In: <i>Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA)</i>. LNCS. ; 2014:25-34. doi:<a href=\"https://doi.org/10.1007/978-3-319-12691-3_3\">10.1007/978-3-319-12691-3_3</a>","mla":"Abshoff, Sebastian, et al. “Randomized Online Algorithms for Set Cover Leasing Problems.” <i>Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA)</i>, 2014, pp. 25–34, doi:<a href=\"https://doi.org/10.1007/978-3-319-12691-3_3\">10.1007/978-3-319-12691-3_3</a>."},"file_date_updated":"2018-03-20T07:12:57Z"}]