A series-parallel matrix is a binary matrix that can be obtained from an empty matrix by successively adjoining rows or columns that are parallel to an existing row/column or have at most one 1-entry. Equivalently, series-parallel matrices are representation matrices of graphic matroids of series-parallel graphs, which can be recognized in linear time. We propose an algorithm that, for an m-by-n matrix A with k nonzeros, determines in expected $\mathcal{O}(m + n + k)$ time whether A is series-parallel, or returns a minimal non-series-parallel submatrix of A. We complement the developed algorithm by an efficient implementation and report about computational results.

翻译：系列-并行矩阵是一类二元矩阵，可从空矩阵通过依次添加与现有行/列平行或至多包含一个1元素的行/列而生成。等价地，系列-并行矩阵是系列-并行图的图拟阵的表示矩阵，可在线性时间内识别。我们提出一种算法，对于具有k个非零元的m×n矩阵A，能在期望$\mathcal{O}(m + n + k)$时间内判定A是否为系列-并行矩阵，或返回A的最小非系列-并行子矩阵。我们通过高效实现补充所开发的算法，并报告计算结果。