  Graph matching aims to find correspondences between two graphs. It is a
fundamental task in pattern recognition. The classical spectral matching
algorithm has time complexity $\mathcal{O}(n^4)$ and space complexity
$\mathcal{O}(n^4)$, where $n$ is the number of nodes. Such a complexity limits
the applicability to large-scale graph matching tasks. This paper proposes an
efficient redesign of spectral matching by transforming the graph matching
problem into a 1D linear assignment problem, which can be solved efficiently by
sorting two $n \times 1$ vectors. The resulting algorithm is named the
lightning spectral assignment method (LiSA), which enjoys a complexity of
$\mathcal{O}(n^2)$. Numerical experiments demonstrate the efficiency and the
theoretical analysis of the strategy.
