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Low-Degree Spanning Trees of Small Weight

Samir Khuller·Balaji Raghavachari·Neal E. Young
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Abstract

The degree-d spanning tree problem asks for a minimum-weight spanning tree in which the degree of each vertex is at most d. When d=2 the problem is TSP, and in this case, the well-known Christofides algorithm provides a 1.5-approximation algorithm (assuming the edge weights satisfy the triangle inequality). In 1984, Christos Papadimitriou and Umesh Vazirani posed the challenge of finding an algorithm with performance guarantee less than 2 for Euclidean graphs (points in R^n) and d > 2. This paper gives the first answer to that challenge, presenting an algorithm to compute a degree-3 spanning tree of cost at most 5/3 times the MST. For points in the plane, the ratio improves to 3/2 and the algorithm can also find a degree-4 spanning tree of cost at most 5/4 times the MST.

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Samir Khuller, Balaji Raghavachari, Neal E. Young. 2002-05-18. Low-Degree Spanning Trees of Small Weight. https://doi.org/10.1137/s0097539794264585

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