Parallel Graph Connected Components via Hyper-Graph Segmentation

The patent segments the graph processing into multiple independent phases (initial labeling, hook passes, compress passes) that can be executed in parallel. Each phase operates on different aspects of the connected components problem, allowing concurrent processing without creating hot spots. The segmentation of the graph data structure into manageable components enables distributed processing across multiple processors while maintaining algorithmic correctness.

The patent introduces an intermediary data structure (the label array and auxiliary arrays) that mediates between the graph data and the processing algorithms. This intermediary layer allows parallel processors to work with local copies of data without directly competing for access to the same memory locations, thereby eliminating hot spots while maintaining the ability to perform parallel operations.

The patent implements local quality by allowing each processor to work with local copies of graph data and maintain local state information. Each processor operates independently on its assigned portion of the graph, accessing only the memory locations relevant to its local computations. This localizes memory access patterns and prevents multiple processors from simultaneously accessing the same memory locations, thereby eliminating hot spots even as processor count increases.

The patent transforms the traditional single-dimension parallel processing approach into a multi-dimensional approach by introducing phase-based processing. Instead of all processors working simultaneously on the same iteration, the algorithm progresses through multiple phases where different subsets of processors work on different aspects of the problem. This dimensional transformation in the processing space allows efficient utilization of multiple processors without creating memory access conflicts.

The patent applies preliminary action by performing initial labeling of all nodes before the main connected components computation begins. Each node is pre-assigned a label and placed in appropriate data structures, preparing the graph for efficient parallel processing. This preliminary setup ensures that when parallel processors begin their work, they can operate independently without needing to perform repeated node visits, thus maintaining the efficiency advantage of sequential algorithms while enabling parallel execution.

The patent implements periodic action through its phased processing approach, where the algorithm alternates between hook passes and compress passes in periodic fashion. Each phase performs a specific function and then transitions to the next phase, allowing systematic progression through the connected components problem. This periodic structure enables parallel processors to work systematically through different aspects of the graph, achieving both parallel speedup and controlled node visitation similar to sequential algorithms.