Fig. 2: The principle of hierarchical clustering for reducing spin and weight complexity.

The number of spins is reduced from \({N}^{2}\) to \(p\times N\), and the weight matrix size is reduced from \({N}^{2}\times {N}^{2}\) to \((p\times N)\times (p\times N)\) by grouping cities into clusters and sub-clusters across hierarchical levels.