Viewing Allocators as Bin Packing Solvers Demystifies Fragmentation

Abstract

This paper presents a trace-based simulation methodology for constructing representations of workload-allocator interaction. We use two-dimensional rectangular bin packing (2DBP) as our foundation. Classical 2DBP algorithms minimize their products' makespan, but virtual memory systems employing demand paging deem such a criterion inappropriate. We view an allocator's placement decisions as a solution to a 2DBP instance, optimizing some unknown criterion particular to that allocator's policy. Our end product is a compact data structure that fits e.g. the simulation of 80 million requests in a 350 MiB file. By design, it is concerned with events residing entirely in virtual memory; no information on memory accesses, indexing costs or any other factor is kept. We bootstrap our contribution's significance by exploring its relationship to maximum resident set size (RSS). Our baseline is the assumption that less fragmentation amounts to smaller peak RSS. We thus define a fragmentation metric in the 2DBP substrate and compute it for 28 workloads linked to 4 modern allocators. We also measure peak RSS for the 112 resulting pairs. Our metric exhibits a strong monotonic relationship (Spearman coefficient $\rho>0.65$) in half of those cases: allocators achieving better 2DBP placements yield $9\%$-$30\%$ smaller peak RSS, with the trends remaining consistent across two different machines. Considering our representation's minimalism, the presented empirical evidence is a robust indicator of its potency. If workload-allocator interplay in the virtual address space suffices to evaluate a novel fragmentation definition, numerous other useful applications of our tool can be studied. Both augmenting 2DBP and exploring alternative computations on it provide ample fertile ground for future research.