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Primal dual based algorithm for degree-balanced spanning tree problem

Author

Listed:
  • Ran, Yingli
  • Chen, Zhihao
  • Tang, Shaojie
  • Zhang, Zhao

Abstract

This paper studies approximation algorithm for the degree-balanced spanning tree (DBST) problem. Given a graph G=(V,E), the goal is to find a spanning tree T such that ∑v ∈ VdegT(v)2 is minimized, where degT(v) denotes the degree of node v in tree T. The idea of taking squares on node degrees is to manifest the role of nodes with large degree, and thus minimizing the sum will result in a comparatively balanced degree distribution. This is a non-linear objective function. We prove that DBST is NP-hard, and then develop a primal–dual based algorithm with a guaranteed performance ratio.

Suggested Citation

  • Ran, Yingli & Chen, Zhihao & Tang, Shaojie & Zhang, Zhao, 2018. "Primal dual based algorithm for degree-balanced spanning tree problem," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 167-173.
    • Handle: RePEc:eee:apmaco:v:316:y:2018:i:c:p:167-173
    DOI: 10.1016/j.amc.2017.08.016
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