Bibliographic record
Abstract
Augmenting an existing sequential data structure with extra information to support greater functionality is a widely used technique. For example, search trees are augmented to build sequential data structures like order-statistic trees, interval trees, tango trees, link/cut trees and many others. We study how to design concurrent augmented tree data structures. We present a new, general technique that can augment a lock-free tree to add any new fields to each tree node, provided the new fields' values can be computed from information in the node and its children. This enables the design of lock-free, linearizable analogues of a wide variety of classical augmented data structures. As a first example, we give a wait-free trie that stores a set S of elements drawn from {0,…,N-1} and supports linearizable order-statistic queries such as finding the kth smallest element of S. Updates and queries take O(log N) steps. We also apply our technique to a lock-free binary search tree (BST), where changes to the structure of the tree make the linearization argument more challenging. Our augmented BST supports order statistic queries in O(h) steps on a tree of height h. The augmentation does not affect the asymptotic step complexity of the updates. As an added bonus, our technique supports arbitrary multi-point queries (such as range queries) with the same step complexity as they would have in the corresponding sequential data structure. For both our trie and BST, we give an alternative augmentation to improve searches and order-statistic queries to run in O(log |S|) steps (at the cost of increasing step complexity of updates by a factor of O(log|S|)).
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.007 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".