Primal dual based algorithm for degree-balanced spanning tree problem

• Published in: Applied mathematics and computation Vol. 316; pp. 167 - 173
• Main Authors: Ran, Yingli, Chen, Zhihao, Tang, Shaojie, Zhang, Zhao
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.01.2018
• Subjects: Degree-balanced spanning tree; Nonlinear objective function; Primal dual algorithm; Primal dual algorithm; Degree-balanced spanning tree; Nonlinear objective function
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2017.08.016

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.