A Network-Flow Technique for Finding Low-Weight Bounded-Degree Spanning Trees
<|reference_start|>A Network-Flow Technique for Finding Low-Weight Bounded-Degree Spanning Trees: 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).<|reference_end|>
@article{fekete2002a,
    title={A Network-Flow Technique for Finding Low-Weight Bounded-Degree Spanning
  Trees},
    author={S. Fekete, S. Khuller, M. Klemmstein, B. Raghavachari, Neal E. Young},
    journal={Journal of Algorithms 24(2):310-324 (1997)},
    year={2002},
    doi={10.1006/jagm.1997.0862},
    archivePrefix={arXiv},
    eprint={cs/0205050},
    primaryClass={cs.DS cs.DM}
}