, Volume 32, Issue 2, pp 237-248

Finding thek smallest spanning trees

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We give improved solutions for the problem of generating thek smallest spanning trees in a graph and in the plane. Our algorithm for general graphs takes timeO(m logβ(m, n)=k 2); for planar graphs this bound can be improved toO(n+k 2). We also show that thek best spanning trees for a set of points in the plane can be computed in timeO(min(k 2 n+n logn,k 2+kn log(n/k))). Thek best orthogonal spanning trees in the plane can be found in timeO(n logn+kn log log(n/k)+k 2).