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：一系列平行矩阵是一个二进制矩阵,可以从空矩阵中通过相邻的行或列获得,这些行或列与现有的行/栏平行,或最多只有1个条目。等量,系列平行矩阵是可线性时间识别的系列平行图的图形模型模型。我们建议一种算法,对于带k非零的 m-bn 矩阵A,在预期的 $\mathcal{O}(m + n + k) 美元时间中确定A是系列单数,还是返回A 中最低限度的非系列单数子子子子子矩阵。我们通过高效的实施和报告计算结果来补充已开发的算法。