Abstract
An algorithm is given to solve the minimum cycle basis problem for regular matroids. The result is based upon Seymour’s decomposition theorem for regular matroids; the Gomory-Hu tree, which is essentially the solution for cographic matroids; and the corresponding result for graphs. The complexity of the algorithm is O((n + m)4), provided that a regular matroid is represented as a binary n × m matrix. The complexity decreases to O((n + m)3.376) using fast matrix multiplication.
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Golynski, A., Horton, J.D. (2002). A Polynomial Time Algorithm to Find the Minimum Cycle Basis of a Regular Matroid. In: Penttonen, M., Schmidt, E.M. (eds) Algorithm Theory — SWAT 2002. SWAT 2002. Lecture Notes in Computer Science, vol 2368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45471-3_21
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DOI: https://doi.org/10.1007/3-540-45471-3_21
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