Scenario-Based Robust Optimization of Tree Structures
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We initiate the study of tree structures in the context of scenario-based robust optimization. Specifically, we study Binary Search Trees (BSTs) and Huffman coding, two fundamental techniques for efficiently managing and encoding data based on a known set of frequencies of keys. Given a number of distinct scenarios, each defined by a frequency distribution over the keys, our objective is to compute a single tree of best-possible performance, relative to any scenario. We consider, as performance metrics, the competitive ratio, which compares multiplicatively the cost of the solution to the tree of least cost among all scenarios, as well as the regret, which induces a similar, but additive comparison. For BSTs, we show that the problem is NP-hard across both metrics. We also obtain an optimal competitive ratio that is logarithmic in the number of scenarios. For Huffman Trees, we likewise prove NP-hardness, and we present an algorithm with logarithmic regret, which we prove to be near-optimal by showing a corresponding lower bound. Last, we give a polynomial-time algorithm for computing Pareto-optimal BSTs with respect to their regret, assuming scenarios defined by uniform distributions over the keys. This setting captures, in particular, the first study of fairness in the context of data structures. We provide an experimental evaluation of all algorithms. To this end, we also provide mixed integer linear program formulation for computing optimal trees.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| 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 | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it