An Almost-Logarithmic Lower Bound for Leader Election with Bounded Value Contention
Bibliographic record
Abstract
We investigate the step complexity of the Leader Election problem (and implementing the corresponding test-and-set object) in asynchronous shared memory, where processes communicate through registers supporting atomic read and write and must coordinate so that a single process becomes the leader. Determining tight step complexity bounds for solving this problem is one of the key open problems in the theory of shared memory distributed computing. The best known algorithm is a randomized tournament-tree, which has worst-case expected step complexity O(log N) for N processes. There are provably no deterministic wait-free algorithms, and only restricted lower bounds are known for obstruction-free and randomized wait-free algorithms. We introduce a new lower bound that establishes an Ω((log N)/(log log N + log Q)) step complexity for any obstruction-free Leader Election algorithm, where N is the number of processes, and 2 ≤ Q ≤ N is a bound on the value contention, which we define as the maximum number of different values that processes can be simultaneously poised to write to the same register in any execution of the algorithm. Our result is strictly stronger than previous bounds based on write contention. In particular, it implies new lower bounds on step complexity that depend on register size.
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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 | 0.004 | 0.027 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.005 | 0.012 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.011 | 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".