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Mathematical Programming

, Volume 169, Issue 1, pp 255–275 | Cite as

Solving the degree-concentrated fault-tolerant spanning subgraph problem by DC programming

  • Chenchen Wu
  • Yishui Wang
  • Zaixin Lu
  • Panos M. Pardalos
  • Dachuan Xu
  • Zhao Zhang
  • Ding-Zhu Du
Full Length Paper Series B

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.

Keywords

Fault-tolerant Connectivity DC programming Convex function 

Mathematics Subject Classification

90C27 90C26 

Notes

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018

Authors and Affiliations

  • Chenchen Wu
    • 1
  • Yishui Wang
    • 2
  • Zaixin Lu
    • 3
  • Panos M. Pardalos
    • 4
  • Dachuan Xu
    • 5
  • Zhao Zhang
    • 6
  • Ding-Zhu Du
    • 7
  1. 1.College of ScienceTianjin University of TechnologyXiqing District, TianjinPeople’s Republic of China
  2. 2.Department of Information and Operations Research, College of Applied SciencesBeijing University of TechnologyBeijingPeople’s Republic of China
  3. 3.School of Engineering and Computer ScienceWashington State UniversityVancouverUSA
  4. 4.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  5. 5.Beijing Institute for Scientific and Engineering ComputingBeijing University of TechnologyBeijingPeople’s Republic of China
  6. 6.College of Mathematics Physics and Information EngineeringZhejiang Normal UniversityJinhuaPeople’s Republic of China
  7. 7.Department of Computer ScienceUniversity of Texa at DallasRichardsonUSA

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