Lower Bounds on the Amortized Time Complexity of Shared Objects
Bibliographic record
Abstract
The amortized step complexity of an implementation measures its performance as a whole, rather than the performance of individual operations. Specifically, the amortized step complexity of an implementation is the average number of steps performed by invoked operations, in the worst case, taken over all possible executions. The point contention of an execution, denoted by $$\dot{c}$$ , measures the maximal number of precesses simultaneously active in the execution. Ruppert (2016) showed that the amortized step complexity of known lock-free implementations for many shared data structures includes an additive factor linear in the point contention $$\dot{c}$$ . This paper shows that there is no lock-free implementation with $$o(\min \{\dot{c}, \sqrt{\log \log n}\})$$ amortized RMR complexity of queues, stacks or heaps from reads, writes, comparison primitives (such as compare &swap) and LL/SC, where n is the total number of the processes in the system. In addition, the paper shows a $$\Omega (\min \{\dot{c}, \log \log n\})$$ lower bound on the amortized step complexity for shared linked lists, skip lists, search trees and other pointer-based data structures. These lower bounds mean that the additive factor linear in $$\dot{c}$$ is inherent for these implementations, provided that the point contention is small compared to the number of processes in the system (i.e. $$\dot{c}\in O(\sqrt{\log \log n})$$ or $$\dot{c}\in O(\log \log n)$$ ).
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.058 |
| Meta-epidemiology (narrow) | 0.004 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.005 | 0.007 |
| Science and technology studies | 0.004 | 0.006 |
| Scholarly communication | 0.011 | 0.023 |
| Open science | 0.009 | 0.008 |
| Research integrity | 0.005 | 0.011 |
| Insufficient payload (model declined to judge) | 0.021 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".