[Paper Review] The Fast Fibonacci Decompression Algorithm

Radim Bača, Václav Snåšel+3 more|ArXiv.org|Dec 5, 2007

Algorithms and Data Compression11 references3 citations

TL;DR

This paper presents a novel Fast Fibonacci Decompression Algorithm that accelerates Fibonacci code decompression by introducing a Fibonacci shift operation, reducing bit-by-bit processing. The method achieves up to 3.5× speedup over the original implementation, particularly beneficial in real-time systems like tree-based data structures where decompression performance is critical.

ABSTRACT

Data compression has been widely applied in many data processing areas. Compression methods use variable-size codes with the shorter codes assigned to symbols or groups of symbols that appear in the data frequently. Fibonacci coding, as a representative of these codes, is used for compressing small numbers. Time consumption of a decompression algorithm is not usually as important as the time of a compression algorithm. However, efficiency of the decompression may be a critical issue in some cases. For example, a real-time compression of tree data structures follows this issue. Tree's pages are decompressed during every reading from a secondary storage into the main memory. In this case, the efficiency of a decompression algorithm is extremely important. We have developed a Fast Fibonacci decompression for this purpose. Our approach is up to $3.5 imes$ faster than the original implementation.

Motivation & Objective

• Address the performance bottleneck in Fibonacci code decompression, especially in real-time systems where decompression speed is critical.
• Overcome the inefficiency of traditional bit-by-bit decompression, which is too slow for high-frequency operations in data structures like B-trees.
• Develop an optimized decompression algorithm that maintains correctness while drastically reducing execution time.
• Introduce a novel Fibonacci shift operation to process multiple bits at once, minimizing memory access and bit-level operations.

Proposed method

• Introduce the Fibonacci shift operation, a new primitive that allows processing multiple bits of a Fibonacci-coded value in a single operation.
• Represent Fibonacci-coded values as sequences of bits ending with '11', leveraging the property that no two adjacent '1's appear in the standard Fibonacci representation.
• Use a record-based data structure to group Fibonacci-coded numbers and their shift offsets, enabling batch processing.
• Apply the Fibonacci shift to extract the value of a Fibonacci-coded segment directly from memory without bit-by-bit scanning.
• Design a decompression loop that accumulates values using the Fibonacci shift and handles carry-over and boundary conditions efficiently.
• Optimize the algorithm to minimize memory access and bit manipulation, focusing on reducing the number of individual bit retrievals from compressed data.

Experimental results

Research questions

• RQ1 Can a novel bit-level operation, the Fibonacci shift, significantly accelerate the decompression of Fibonacci-coded integers?
• RQ2 How does the performance of the proposed Fast Fibonacci Decompression algorithm compare to the original bit-by-bit decompression method in real-world workloads?
• RQ3 Does the speedup remain consistent across different data distributions, such as sequential and random number sequences?
• RQ4 To what extent does the algorithm's efficiency improve in memory-constrained, real-time systems like database index structures?
• RQ5 Can the Fibonacci shift operation be generalized to other prefix codes with similar structural constraints?

Key findings

• The Fast Fibonacci Decompression Algorithm achieves a maximum speedup of 4.18× on sequential collections of very large numbers, with an average speedup of 3.73× across all sequential test cases.
• For random number collections, the algorithm achieves an average speedup of 3.52×, demonstrating consistent performance gains regardless of data distribution.
• The algorithm maintains a speedup of over 3.5× for individual numbers across all tested values, as confirmed by decoding time measurements in Figure 2.
• The proposed method reduces decompression time from 1,109 ms (original) to 265 ms (fast) for the largest sequential dataset of 4,194,304 numbers.
• The Fibonacci shift operation effectively eliminates the need for per-bit processing, reducing memory access overhead and improving data-level parallelism.
• The algorithm is robust and efficient across all number ranges, from 8-bit to 32-bit integers, proving its universality and practicality in real-time systems.