Generalized Deduplication: Bounds, Convergence, and Asymptotic Properties (1901.02720v4)

Abstract: We study a generalization of deduplication, which enables lossless deduplication of highly similar data and show that standard deduplication with fixed chunk length is a special case. We provide bounds on the expected length of coded sequences for generalized deduplication and show that the coding has asymptotic near-entropy cost under the proposed source model. More importantly, we show that generalized deduplication allows for multiple orders of magnitude faster convergence than standard deduplication. This means that generalized deduplication can provide compression benefits much earlier than standard deduplication, which is key in practical systems. Numerical examples demonstrate our results, showing that our lower bounds are achievable, and illustrating the potential gain of using the generalization over standard deduplication. In fact, we show that even for a simple case of generalized deduplication, the gain in convergence speed is linear with the size of the data chunks.

• The paper establishes tight upper and lower bounds on encoded sequence lengths, underscoring its potential for significant storage cost reduction.
• The analysis reveals that generalized deduplication achieves near-source entropy per chunk with minimal overhead and remarkably faster convergence.
• Empirical simulations validate the theoretical findings, demonstrating improved compression efficiency in handling highly similar datasets.

Essay on "Generalized Deduplication: Bounds, Convergence, and Asymptotic Properties"

The paper "Generalized Deduplication: Bounds, Convergence, and Asymptotic Properties" presents a thorough investigation into a generalization of the deduplication compression technique, extending its application to highly similar data. This generalization allows for lossless deduplication while ensuring faster convergence and efficient compression. The authors argue that traditional deduplication with fixed chunk length is a special case of their proposed approach.

Contributions

The primary contributions of this work are threefold: establishing bounds on the expected length of encoded sequences, analyzing the asymptotic behavior, and providing empirical results demonstrating the practical efficiency of the generalized technique.

1. Bounds: The authors present a formal model for generalized deduplication, treating it as a source coding technique. They derive upper and lower bounds on the expected length of coded sequences. The work quantifies the potential advantage of generalized deduplication over the classic approach by highlighting a significant reduction in compression storage costs given data that fits the proposed model.
2. Asymptotic Behavior: A detailed exploration of the asymptotic costs reveals that generalized deduplication can achieve near-source entropy per chunk, with only minimal overhead. The analysis shows a notable speed in convergence for generalized deduplication, which translates to better performance in practical scenarios where data availability is limited.
3. Numerical Results: The paper offers numerical simulations that validate the theoretical results. The bounds on expected sequence length and convergence speed are visualized, demonstrating the practical gains in storage costs when using generalized deduplication over classic deduplication. Notably, the paper shows that even simple instances of generalized deduplication achieve a linear gain in convergence speed relative to the size of the data chunks.

Methodology

The generalized deduplication technique is framed as an efficient source coding approach. It operates on sequences of binary data, identifying chunks through a combination of base patterns and deviations. This process is supported by a mapping function that aids in the identification of a chunk's base, allowing deduplication to accommodate near-identical data. The generalized approach thereby extends the applicability of deduplication methods to scenarios where data undergoes slight variations, such as environmental data from IoT devices.

The core of the deduplication process involves constructing a dictionary of encountered bases, which is updated dynamically. This technique reduces redundancy more effectively than the classic approach by accounting for minute deviations, offering significant storage cost reductions, especially vital in handling large-scale datasets.

Implications and Future Work

The implications of this research extend to both theoretical and practical dimensions. On a theoretical level, the paper provides a deeper understanding of the fundamental limits of deduplication techniques, expanding the scope of information theory in compression methods. Practically, the enhanced convergence and storage efficiency make this approach suitable for a wide array of storage systems, particularly in applications dealing with extensive and similar datasets.

The proposed method serves as a promising avenue for further research, particularly in the context of adapting this model to non-uniform data distributions. Future work might explore tailored adjustments of the generalized model to more accurately fit practical data scenarios. Additionally, the development of adaptive techniques to automate the determination of bases and deviations from empirical data will enhance the usability of generalized deduplication in real-world applications.

Overall, this paper lays a strong foundation for advancing deduplication techniques, presenting a rigorous analysis that underscores both the theoretical and practical potential of generalized deduplication for efficient data compression.