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Packing feedback arc sets in reducible flow graphs

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Abstract

In this paper we establish a min–max relation in arc-weighted reducible flow graphs. In particular, we prove that the maximum cardinality of feedback arc set packings equals the minimum total weight of cycles. We also present an \(O(n^2 m)\) algorithm for finding a maximum feedback arc set packing in reducible flow graphs.

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Notes

  1. ‘First available’ here refers to the unused \(r-t\) cut \(\partial ^+(U_i)\) with the least index i.

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Acknowledgments

The author would like to thank Prof. Wenan Zang for his invaluable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, The University of Hong Kong, Hong Kong, China

    Han Xiao

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  1. Han Xiao
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Correspondence to Han Xiao.

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Xiao, H. Packing feedback arc sets in reducible flow graphs. J Comb Optim 32, 951–959 (2016). https://doi.org/10.1007/s10878-015-9922-6

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  • DOI: https://doi.org/10.1007/s10878-015-9922-6

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