A Fast Hierarchical Adaptive Analog Routing Algorithm Based on Integer Linear Programming
Bibliographic record
Abstract
The shrinking design window and high parasitic sensitivity in advanced technologies have imposed special challenges on analog and radio frequency (RF) integrated circuit design. The state-of-the-art analog routing research tends to favor linear programming to achieve various analog constraints, which, although effective, fail to offer high routing efficiency on its own. In this article, we propose a new methodology to address such a deficiency based on integer linear programming (ILP) but without compromising the capability of handling any special constraints for the analog routing problems. Our proposed method supports hierarchical routing, which can divide the entire routing area into multiple small heterogeneous regions where the ILP can efficiently derive routing solutions. Distinct from the conventional methods, our algorithm utilizes adaptive resolutions for various routing regions. For a more congested region, a routing grid with higher resolution is employed, whereas a lower-resolution grid is adopted to a less-crowded routing region. For a large empty space, routing efficiency can be even boosted by creating more routing hierarchy levels. This scheme is especially beneficial to the analog and RF layouts, which are far sparser than their digital counterparts. The experimental results show that our proposed adaptive ILP-based router is much faster than the conventional ones, since it spends much less time in the areas that need no accurate routing anyway. The higher efficiency is demonstrated for large circuits and especially sparse layouts along with promising routing quality in terms of analog constraints.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".