Intermediate Value Linearizability: A Quantitative Correctness Criterion

Big data processing systems often employ batched updates and sketches to estimate certain properties of large data. For example, a CountMin sketch approximates the frequencies at which elements occur in stream, counter counts events batches. This paper focuses on correctness criteria for concurrent implementations such objects. Specifically, we consider quantitative objects, whose return values are from an ordered domain, with particular emphasis (ϵ, δ )-bounded objects that numerical quantity error most ϵ probability least 1 − . The de facto criterion is linearizability. Intuitively, under linearizability, when read overlaps update, it must object’s value either before update or after it. Consider, single increment operation three new events, bumping counter’s 7 10. In linearizable implementation counter, overlapping this We observe, however, typical use cases, any intermediate between 10 would also be acceptable. To capture additional degree freedom, propose Intermediate Value Linearizability (IVL) , relaxes linearizability allow returning values, instance 8 example above. Roughly speaking, IVL allows reads bounded two legal A key feature can prove themselves )-bounded. illustrate power result, give straightforward efficient sketch, (albeit not linearizable). present four examples each showcasing different way using IVL. first simple wait-free O (1) step complexity update. next considers further shows how relax notion r -relaxation. Our third non-atomic iterator over structure. augment structure auxiliary history variable state includes “tombstones” items deleted Here, semantics required augmented level. Finally, priority queue show some require paired other criteria; indeed natural coupled sequential consistency. Lastly, inherently cheaper than ones. particular, lower bound Ω ( n ) single-writer multi-reader registers, more expensive our implementation.