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Online Paging with Heterogeneous Cache Slots

Authors Marek Chrobak, Samuel Haney, Mehraneh Liaee, Debmalya Panigrahi, Rajmohan Rajaraman, Ravi Sundaram, Neal E. Young

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Author Details

Marek Chrobak
  • University of California at Riverside, CA, USA
Samuel Haney
  • Tumult Labs, Durham, NC, USA
Mehraneh Liaee
  • Northeastern University, Boston, MA, USA
Debmalya Panigrahi
  • Duke University, Durham, NC, USA
Rajmohan Rajaraman
  • Northeastern University, Boston, MA, USA
Ravi Sundaram
  • Northeastern University, Boston, MA, USA
Neal E. Young
  • University of California at Riverside, CA, USA

Funding

  • Chrobak, Marek: Supported by NSF grants CCF-1536026 and CCF-2153723.
  • Haney, Samuel: Supported by NSF grants CCF-1527084 and CCF-1535972.
  • Liaee, Mehraneh: Supported by NSF grants CCF-1535929 and CCF-1909363.
  • Panigrahi, Debmalya: Supported by NSF grants CCF-1527084, CCF-1535972, CCF-1750140, CCF-1955703, ARO grant W911NF2110230, and Indo-US Joint Center for Algorithms under Uncertainty.
  • Rajaraman, Rajmohan: Supported by NSF grants CCF-1535929 and CCF-1909363.
  • Sundaram, Ravi: Supported by NSF grants CCF-1535929 and IIS-2039945.
  • Young, Neal E.: Supported by NSF grant CCF-1619463.

Cite As Get BibTex

Marek Chrobak, Samuel Haney, Mehraneh Liaee, Debmalya Panigrahi, Rajmohan Rajaraman, Ravi Sundaram, and Neal E. Young. Online Paging with Heterogeneous Cache Slots. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 23:1-23:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.STACS.2023.23

Abstract

It is natural to generalize the online k-Server problem by allowing each request to specify not only a point p, but also a subset S of servers that may serve it. To initiate a systematic study of this generalization, we focus on uniform and star metrics. For uniform metrics, the problem is equivalent to a generalization of Paging in which each request specifies not only a page p, but also a subset S of cache slots, and is satisfied by having a copy of p in some slot in S. We call this problem Slot-Heterogenous Paging.
In realistic settings only certain subsets of cache slots or servers would appear in requests. Therefore we parameterize the problem by specifying a family 𝒮 ⊆ 2^[k] of requestable slot sets, and we establish bounds on the competitive ratio as a function of the cache size k and family 𝒮. If all request sets are allowed (𝒮 = 2^[k]), the optimal deterministic and randomized competitive ratios are exponentially worse than for standard Paging (𝒮 = {[k]}). As a function of |𝒮| and k, the optimal deterministic ratio is polynomial: at most O(k²|𝒮|) and at least Ω(√{|𝒮|}). For any laminar family {𝒮} of height h, the optimal ratios are O(hk) (deterministic) and O(h²log k) (randomized). The special case that we call All-or-One Paging extends standard Paging by allowing each request to specify a specific slot to put the requested page in. For All-or-One Paging the optimal competitive ratios are Θ(k) (deterministic) and Θ(log k) (randomized), while the offline problem is NP-hard. We extend the deterministic upper bound to the weighted variant of All-or-One Paging (a generalization of standard Weighted Paging), showing that it is also Θ(k).
Some results for the laminar case are shown via a reduction to the generalization of Paging in which each request specifies a set P of pages, and is satisfied by fetching any page from P into the cache. The optimal ratios for the latter problem (with laminar family of height h) are at most hk (deterministic) and hH_k (randomized).

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
Keywords
  • Caching and paging algorithms
  • k-server
  • weighted paging
  • laminar family

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