Physical Sciences and Mathematics Commons^™

Low-Degree Spanning Trees Of Small Weight, Samir Khuller, Balaji Raghavachari, Neal Young

Dartmouth Scholarship

Given n points in the plane, the degree-K spanning-tree problem asks for a spanning tree of minimum weight in which the degree of each vertex is at most K. This paper addresses the problem of computing low-weight degree-K spanning trees for $K > 2$. It is shown that for an arbitrary collection of n points in the plane, there exists a spanning tree of degree 3 whose weight is at most 1.5 times the weight of a minimum spanning tree. It is shown that there exists a spanning tree of degree 4 whose weight is at most 1.25 times …