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：串并联矩阵是一种二元矩阵，可以通过从空矩阵出发，反复邻接与现有行或列并行或至多包含一个 1 条目的行或列来得到。等价地，串并联矩阵是串并联图的图拟阵的表示矩阵，这类矩阵可在 O(n) 时间内被识别。我们提出一种算法，对于具有 k 个非零元素的 m×n 矩阵 A，该算法可在期望 O(m + n + k) 时间内判定 A 是否为串并联矩阵，或返回 A 的一个最小非串并联子矩阵。我们通过高效实现对所开发的算法进行补充，并报告计算结果。