Efficient Caching with Reserves via Marking

Authors Sharat Ibrahimpur , Manish Purohit , Zoya Svitkina, Erik Vee, Joshua R. Wang

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Sharat Ibrahimpur
  • Department of Mathematics, London School of Economics and Political Science, UK
Manish Purohit
  • Google Research, USA
Zoya Svitkina
  • Google Research, USA
Erik Vee
  • Google Research, USA
Joshua R. Wang
  • Google Research, USA

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Sharat Ibrahimpur, Manish Purohit, Zoya Svitkina, Erik Vee, and Joshua R. Wang. Efficient Caching with Reserves via Marking. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 80:1-80:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Caching and paging algorithms
  • Approximation Algorithms
  • Online Algorithms
  • Caching


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