A Network-Flow Technique for Finding Low-Weight Bounded-Degree Spanning Trees
摘要
The problem considered is the following. Given a graph with edge weights satisfying the triangle inequality, and a degree bound for each vertex, compute a low-weight spanning tree such that the degree of each vertex is at most its specified bound. The problem is NP-hard (it generalizes Traveling Salesman (TSP)). This paper describes a network-flow heuristic for modifying a given tree T to meet the constraints. Choosing T to be a minimum spanning tree (MST) yields approximation algorithms with performance guarantee less than 2 for the problem on geometric graphs with L_p-norms. The paper also describes a Euclidean graph whose minimum TSP costs twice the MST, disproving a conjecture made in ``Low-Degree Spanning Trees of Small Weight'' (1996).
引用
@article{arxiv.cs/0205050,
title = {A Network-Flow Technique for Finding Low-Weight Bounded-Degree Spanning Trees},
author = {S. Fekete and S. Khuller and M. Klemmstein and B. Raghavachari and Neal E. Young},
journal= {arXiv preprint arXiv:cs/0205050},
year = {2015}
}