Recognizing Series-Parallel Matrices in Linear Time

Matthias Walter ()
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Matthias Walter: Department of Applied Mathematics, University of Twente, 7522 NB Enschede, Netherlands

INFORMS Journal on Computing, 2023, vol. 35, issue 6, 1404-1418

Abstract: 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 O ( m + n + k ) implementation and report about computational results.

Keywords: series-parallel; recognition algorithm; matroids (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:35:y:2023:i:6:p:1404-1418

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