A Network-Flow Technique for Finding Low-Weight Bounded-Degree Spanning Trees

Details A Network-Flow Technique for Finding Low-Weight Bounded-Degree Spanning Trees A Network-Flow Technique for Finding Low-Weight Bounded-Degree Spanning Trees

2002-05-18

arxiv.org/abs/cs/0205050v1

Journal of Algorithms 24(2):310-324 (1997)

Computer Science

Data Structures and Algorithms

Scientific paper

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).

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