Beehive: Erasure Codes for Fixing Multiple Failures in Distributed Storage Systems
Bibliographic record
Abstract
In distributed storage systems, erasure codes have been increasingly deployed to tolerate server failures without loss of data. Traditional erasure codes, such as Reed-Solomon codes, suffer from a high volume of network transfer and disk I/O to recover unavailable data at failed storage servers. Typically, unavailable data at different failed storage servers in a distributed storage system are fixed separately. It has been shown that it is possible to reduce the volume of network transfer significantly by reconstructing data from multiple storage servers at the same time. However, there has been no construction of erasure codes to achieve it without imposing strict constraints on system parameters. In this paper, we propose Beehive codes, designed for optimizing the volume of network transfers to fix the data on multiple failed storage servers. Beehive codes can be constructed over a wide range of system parameters at code rate no more than 0.5, while incurring slightly more storage overhead than Reed-Solomon codes. To achieve the optimal storage overhead as Reed-Solomon codes, we further extend vanilla Beehive codes to MDS Beehive codes, which incurs near-optimal volumes of network transfers during reconstruction. We implement both Beehive and MDS Beehive Codes in C++ and evaluate their performance on Amazon EC2. Our evaluation results have clearly shown that the volume of both network transfers and disk I/O can be conserved by a substantial margin.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".