Pipelining Kruskal's: A Neuromorphic Approach for Minimum Spanning Tree

TL;DR

The paper tackles efficient MST computation on large graphs within neuromorphic hardware by introducing an SNN-based union-find and a pipelined Kruskal algorithm that overlaps neuromorphic sorting (NeuroSort/NeuroRadixSort) with union-find. It extends neuromorphic complexity analysis to account for structural plasticity and demonstrates, on the DIMACS10 dataset, that a pipelined Kruskal can achieve substantial speedups over Prim-based neuromorphic approaches (up to $1283.80\times$, median $\approx 540.76\times$). The work also analyzes when pipelining is advantageous versus when the MST edge enumeration bottleneck dominates, providing practical guidance for hardware deployment. Overall, it demonstrates a viable, energy-aware route to massively parallel MST acceleration on neuromorphic platforms, with clear architectural and algorithmic tradeoffs and results grounded in large-scale graphs. The study further contributes a refined complexity framework that integrates dynamic synaptic plasticity into performance analysis, laying groundwork for future neuromorphic graph algorithms.

Abstract

Neuromorphic computing, characterized by its event-driven computation and massive parallelism, is particularly effective for handling data-intensive tasks in low-power environments, such as computing the minimum spanning tree (MST) for large-scale graphs. The introduction of dynamic synaptic modifications provides new design opportunities for neuromorphic algorithms. Building on this foundation, we propose an SNN-based union-sort routine and a pipelined version of Kruskal's algorithm for MST computation. The event-driven nature of our method allows for the concurrent execution of two completely decoupled stages: neuromorphic sorting and union-find. Our approach demonstrates superior performance compared to state-of-the-art Prim 's-based methods on large-scale graphs from the DIMACS10 dataset, achieving speedups by 269.67x to 1283.80x, with a median speedup of 540.76x. We further evaluate the pipelined implementation against two serial variants of Kruskal's algorithm, which rely on neuromorphic sorting and neuromorphic radix sort, showing significant performance advantages in most scenarios.

Figures (6)

• Figure 1: Symbolic notation for a typical SNN
• Figure 2: SNN of NeuroSort
• Figure 3: SNN of UnionFind (sequential)
• Figure 4: SNN of Pipe
• Figure 5: Speedup comparison between SeqNeuro, SeqRadix and Pipe on DIMACS10 dataset