Primal dual based algorithm for degree-balanced spanning tree problem

摘要

This paper studies approximation algorithm for the degree-balanced spanning tree (DBST) problem. Given a graph 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.