Abstract
In this paper, we consider the maximum and minimum versions of degree-concentrated fault-tolerant spanning subgraph problem which has many applications in network communications. We prove that both this two problems are NP-hard. For the maximum version, we use DC programming relaxation to propose a heuristic algorithm. Numerical tests indicate that the proposed algorithm is efficient and effective. For the minimum version, we also formulate it as a DC program, and show that the DC algorithm does not perform well for this problem.
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Acknowledgements
The first author was partially supported by NSFC (No. 11501412). The fourth author was partially supported by the Paul and Heidi Brown Preeminent Professorship at ISE, University of Florida. The fifth author was partially supported by NSFC (No. 11531014). The sixth author was partially supported by NSFC (Nos. 61222201 and 11531011).
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Wu, C., Wang, Y., Lu, Z. et al. Solving the degree-concentrated fault-tolerant spanning subgraph problem by DC programming. Math. Program. 169, 255–275 (2018). https://doi.org/10.1007/s10107-018-1242-z
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DOI: https://doi.org/10.1007/s10107-018-1242-z