Feed-Forward Merge Pipeline for Skew-Resilient Data Sorting

The patent segments the K-way merging problem into multiple 2-way merging stages. Instead of implementing a complex K-way merge tree with O(K) state, the invention divides the K input lists into groups and performs sequential 2-way merges at each stage. This segmentation reduces the tournament state requirement from O(K) to O(1) per stage while achieving the same log2K reduction in merging passes through the multi-stage approach.

The patent employs periodic action by implementing multiple 2-way merging stages that operate in sequence. Each stage processes a subset of the K lists through repeated 2-way merges, creating a periodic pattern of merge operations. This approach maintains high utilization by keeping the tournament state minimal and avoiding the compute/latency bottlenecks that occur in single-stage K-way merges, while still achieving the log2K reduction in total merging passes through the staged periodic operations.

The patent applies dynamics by making the merging process adaptive to distribution skew through multiple 2-way merging stages. At each stage, the algorithm dynamically selects which lists to merge based on current data characteristics, rather than following a fixed merge tree structure. This dynamic approach allows the system to handle skewed distributions effectively while maintaining high throughput across multiple processing elements, as each stage can adjust to the actual data distribution encountered.

The patent extracts the complex flow management mechanisms (deep buffering, backpressure signaling, rate converters) from the merging architecture and replaces them with simple 2-way merging stages. By taking out these complicated components and using straightforward sequential 2-way merges instead, the invention achieves adaptability to distribution skew through the staged approach without incurring the heavy implementation overhead of sophisticated flow management systems.