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Recognizing Series-Parallel Matrices in Linear Time

Author

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  • Matthias Walter

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

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.

Suggested Citation

  • Matthias Walter, 2023. "Recognizing Series-Parallel Matrices in Linear Time," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1404-1418, November.
    • Handle: RePEc:inm:orijoc:v:35:y:2023:i:6:p:1404-1418
    DOI: 10.1287/ijoc.2021.0233
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    References listed on IDEAS

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    1. Wei Chen & Milind Dawande & Ganesh Janakiraman, 2014. "Integrality in Stochastic Inventory Models," Production and Operations Management, Production and Operations Management Society, vol. 23(9), pages 1646-1663, September.
    2. Robert E. Bixby & Donald K. Wagner, 1988. "An Almost Linear-Time Algorithm for Graph Realization," Mathematics of Operations Research, INFORMS, vol. 13(1), pages 99-123, February.
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