# Recognizing Series-Parallel Matrices in Linear Time



A series-parallel matrix is a binary matrix that can be obtained from an empty matrix by successively adjoining rows or columns that are copies of 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.