A Nearly Quadratic Improvement for Memory Reallocation
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3626183.3659965.pdf
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Author(s)
Farach-Colton, Martin
Kuszmaul, William
Sheffield, Nathan S.
Westover, Alek
Date Issued
June 17, 2024
Publisher
ACM|Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures
Citation
Farach-Colton, Martin, Kuszmaul, William, Sheffield, Nathan S. and Westover, Alek. 2024. "A Nearly Quadratic Improvement for Memory Reallocation."
Version
Final published version
Abstract
In the Memory Reallocation Problem a set of items of various sizes must be dynamically assigned to non-overlapping contiguous chunks of memory. It is guaranteed that the sum of the sizes of all items present at any time is at most a (1-ε)-fraction of the total size of memory (i.e., the load-factor is at most 1-ε). The allocator receives insert and delete requests online, and can re-arrange existing items to handle the requests, but at a reallocation cost defined to be the sum of the sizes of items moved divided by the size of the item being inserted/deleted.
The folklore algorithm for Memory Reallocation achieves a cost of O(ε-1) per update. In recent work at FOCS'23, Kuszmaul showed that, in the special case where each item is promised to be smaller than an ε4-fraction of memory, it is possible to achieve expected update cost O(logε-1). Kuszmaul conjectures, however, that for larger items the folklore algorithm is optimal.
In this work we disprove Kuszmaul's conjecture, giving an allocator that achieves expected update cost O(ε-1/2*polylog ε-1) on any input sequence. We also give the first non-trivial lower bound for the Memory Reallocation Problem: we demonstrate an input sequence on which any resizable allocator (even offline ) must incur amortized update cost at least Ω(logε-1).
Finally, we analyze the Memory Reallocation Problem on a stochastic sequence of inserts and deletes, with random sizes in [δ, 2 δ] for some δ. We show that, in this simplified setting, it is possible to achieve O(logε-1 ) expected update cost, even in the "large-item" parameter regime (δ > ε4).
Description
SPAA ’24, June 17–21, 2024, Nantes, France
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DOI of Published Version
https://doi.org/10.1145/3626183.3659965
