Binary Insertion Sort for Hardware Acceleration: Balancing Flexibility and Resource Efficiency
Bibliographic record
Abstract
This paper presents Binary Insertion Sort (BIS), a parallel-friendly sorting algorithm optimized for hardware implementation. By enabling up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k=\left\lceil\log _{2}(N-1)\right\rceil$</tex> concurrent binary searches, BIS targets a theoretical time complexity of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{O}(N)$</tex>, offering an efficient alternative to comparator-intensive designs. Comparative evaluations against state-of-the-art hard-ware sorting methods, including DL Sort and OWS, show that BIS reduces comparison operations by up to 50% relative to DL Sort while requiring only <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{O}(\log N)$</tex> comparators, significantly lowering hardware complexity. Although OWS achieves minimal data movement, its strict dependence on bit-width and input size limits its general applicability. BIS, by contrast, provides a more flexible and scalable architecture, balancing performance, resource efficiency, and adaptability. These qualities position BIS as a strong candidate for integration in real-time and resource-constrained systems.
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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 | 0.001 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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 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".