Online Paging with Heterogeneous Cache Slots
Marek Chrobak, Samuel Haney, Mehraneh Liaee, Debmalya Panigrahi,, Rajmohan Rajaraman, Ravi Sundaram, and Neal E. Young

TL;DR
This paper introduces and analyzes the Slot-Heterogeneous Paging problem, a generalization of classic paging with requests specifying subsets of cache slots, providing bounds on competitive ratios based on family structure and cache size.
Contribution
It establishes bounds on competitive ratios for Slot-Heterogeneous Paging, including special cases like laminar families and All-or-One Paging, extending understanding of paging variants.
Findings
Optimal deterministic ratio is polynomial in cache size and family size.
Exponential worst-case ratios for full request set families.
Laminar families yield near-linear bounds on ratios.
Abstract
It is natural to generalize the online -Server problem by allowing each request to specify not only a point , but also a subset of servers that may serve it. For uniform metrics, the problem is equivalent to a generalization of Paging in which each request specifies not only a page , but also a subset of cache slots, and is satisfied by having a copy of in some slot in . We call this problem Slot-Heterogenous Paging. We parameterize the problem by specifying a family of requestable slot sets, and we establish bounds on the competitive ratio as a function of the cache size and family : - If all request sets are allowed (), the optimal deterministic and randomized competitive ratios are exponentially worse than for standard \Paging (). - As a function…
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