Exact Perfect Matching Oracles for k-Regular Bipartite Graphs on Low-Resource Hardware: Ground Truth for Neural Network Topology Pruning

Structured pruning of neural networks operating on k-regular layer architectures requires enumerating all valid weight configurations that preserve full inter-layer connectivity. This problem is precisely the permanent of the N x N bipartite adjacency matrix a #P-complete computation that has been considered intractable on commodity hardware, forcing practitioners to rely on stochastic heuristics with no guaranteed coverage of the solution space.

We present a shared-nothing parallel implementation of Glynn's formula traversed by binary reflected Gray code, extended with arithmetic to support dense k-regular graphs (K \ge 7). The engine is validated against the Leibniz brute-force permanent across 20 test cases identity matrices, complete bipartite $K{N,N}$, random dense matrices, and k-regular bipartite graphs for K \in \{2,3,4\} and N \in \{4,...,10\}.