Selection of Supervised Learning-Based Sparse Matrix Reordering Algorithms

Sparse matrix reordering is a key optimization strategy commonly used in large-scale sparse matrix solvers. By permuting the rows and columns of a matrix, it aims to reduce the matrix bandwidth or minimize fill-in during factorization, thereby improving computational efficiency. Traditional algorithm selection typically relies on brute-force search or empirical heuristics, which cannot adapt to the structural variety of different sparse matrices. To address this, we propose a supervised-learning-based model for selecting sparse matrix reordering algorithms. By learning the mapping between various matrix features and popular reordering methods, our model automates and intelligently chooses the most suitable algorithm. Experiments on the SuiteSparse matrix collection demonstrate that our model achieves high prediction accuracy for the optimal reordering method of each matrix. Compared to AMD, the predominant ordering algorithm in practice, our model achieves a 55.37% reduction in solution time with an average speedup ratio of 1.45.