Online caching is among the most fundamental and well-studied problems in the area of online algorithms. Innovative algorithmic ideas and analysis - including potential functions and primal-dual techniques - give insight into this still-growing area. Here, we introduce a new analysis technique that first uses a potential function to upper bound the cost of an online algorithm and then pairs that with a new dual-fitting strategy to lower bound the cost of an offline optimal algorithm. We apply these techniques to the Caching with Reserves problem recently introduced by Ibrahimpur et al. [Ibrahimpur et al., 2022] and give an O(log k)-competitive fractional online algorithm via a marking strategy, where k denotes the size of the cache. We also design a new online rounding algorithm that runs in polynomial time to obtain an O(log k)-competitive randomized integral algorithm. Additionally, we provide a new, simple proof for randomized marking for the classical unweighted paging problem.
@InProceedings{ibrahimpur_et_al:LIPIcs.ICALP.2023.80, author = {Ibrahimpur, Sharat and Purohit, Manish and Svitkina, Zoya and Vee, Erik and Wang, Joshua R.}, title = {{Efficient Caching with Reserves via Marking}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {80:1--80:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.80}, URN = {urn:nbn:de:0030-drops-181328}, doi = {10.4230/LIPIcs.ICALP.2023.80}, annote = {Keywords: Approximation Algorithms, Online Algorithms, Caching} }
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