A Set Cover Based Efficient Solution for the Complementary Index Coding Problem
Bibliographic record
Abstract
The Index Coding problem can be considered as one of the basic problems in information theory. In this problem a relay node needs to deliver a set of packets to a set of client over a broadcast wireless channel. Each client might posses some "side information" related to the transmissions by the relay node. The goal is to minimize number of transmissions from the relay node by taking advantage of the side information. The Index Coding problem has been proven to be NP-hard and NP-hard to approximate. The Complementary Index Coding problem is a complementary problem of the Index Coding problem. In the Complementary Index Coding problem the objective is to maximize number of the saved transmissions, i.e., the number of transmissions that are saved by encoding packets compared to the solution that does not perform coding. This work aims at improving the gains of the Complementary Index Coding problem by proposing a Set Cover based solution that guarantees an approximation ratio of 1/(1-(H_k|S|/n)). Moreover, we propose a scheme for transforming the Index Coding problem in to the Set Cover problem. In addition to this, we compare the proposed algorithm with the current state of the art. The experimental results show that the proposed solution out performs current state of the art both in terms of coding advantage as well as running time.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".