Non-Linear Paging

We formulate and study non-linear paging - a broad model of online paging where the size of subsets of pages is determined by a monotone non-linear set function of the pages. This model captures the well-studied classic weighted paging and generalized paging problems, and also submodular and supermo...

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Bibliographic Details
Published inarXiv.org
Main Authors Doron-Arad, Ilan, Joseph, Naor
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.04.2024
Subjects
Algorithms
Lower bounds
Machine learning
Mathematical models
Paging
Parameters
Upper bounds
Virtual memory systems
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Summary:We formulate and study non-linear paging - a broad model of online paging where the size of subsets of pages is determined by a monotone non-linear set function of the pages. This model captures the well-studied classic weighted paging and generalized paging problems, and also submodular and supermodular paging, studied here for the first time, that have a range of applications from virtual memory to machine learning. Unlike classic paging, the cache threshold parameter \(k\) does not yield good competitive ratios for non-linear paging. Instead, we introduce a novel parameter \(\ell\) that generalizes the notion of cache size to the non-linear setting. We obtain a tight deterministic \(\ell\)-competitive algorithm for general non-linear paging and a \(o\left(\log^2 (\ell)\right)\)-competitive lower bound for randomized algorithms. Our algorithm is based on a new generic LP for the problem that captures both submodular and supermodular paging, in contrast to LPs used for submodular cover settings. We finally focus on the supermodular paging problem, which is a variant of online set cover and online submodular cover, where sets are repeatedly requested to be removed from the cover. We obtain polylogarithmic lower and upper bounds and an offline approximation algorithm.
ISSN:2331-8422