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 one-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 time whether A is series-parallel or returns a minimal non–series-parallel submatrix of A. We complement the developed algorithm by an efficient $\mathcal{O}(m+n+k)$implementation and report about computational results.

History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete.

Funding: This work was supported by Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant OCENW.M20.151].

Supplemental Material: The software that supports the findings of this study is available at the GitHub software repository (https://github.com/discopt/cmr-series-parallel).