Fast Prefix Sums for Data Compression and Join Algorithms

In this article, we explore the concept of data compression using differential encoding, a technique that has shown great promise in reducing the size of data sets while maintaining their integrity. We start by defining what differential encoding is and how it works, before delving into the various approaches to data compression using this method.
One of the key findings in our survey is that prefix sums play a crucial role in data compression. By representing a set of data elements as a sum of smaller prefix sums, we can significantly reduce the size of the data set while preserving its original content. In fact, prefix sums can account for the majority of the running time in data compression algorithms that use differential encoding.
To implement these algorithms efficiently, we need to carefully choose the right configuration parameters, such as the dilation factor. While it may seem tempting to increase this parameter to achieve faster performance, our findings suggest that getting the configuration parameters just right is crucial for optimal performance. Moreover, partitioning the data can also significantly improve the performance of these algorithms.
We present several examples of prefix sum algorithms, including ones that use two sweeps over a balanced tree, and others that accumulate prefix sums incrementally. These algorithms demonstrate the efficiency and versatility of differential encoding in compressing large datasets.
In conclusion, our survey highlights the potential of data compression using differential encoding to reduce the size of data sets while maintaining their integrity. By carefully choosing the right configuration parameters and leveraging partitioning techniques, we can significantly improve the performance of these algorithms. As the amount of data continues to grow exponentially, efficient data compression methods like differential encoding are becoming increasingly important for a wide range of applications, from scientific research to everyday computing.