# Finding the*k* smallest spanning trees

Algorithm Theory

- Received:
- Revised:

DOI: 10.1007/BF01994879

- Cite this article as:
- Eppstein, D. BIT (1992) 32: 237. doi:10.1007/BF01994879

## Abstract

We give improved solutions for the problem of generating the*k* smallest spanning trees in a graph and in the plane. Our algorithm for general graphs takes time*O*(*m* log*β*(*m, n*)=*k*^{2}); for planar graphs this bound can be improved to*O*(*n*+*k*^{2}). We also show that the*k* best spanning trees for a set of points in the plane can be computed in time*O*(min(*k*^{2}*n*+*n* log*n*,*k*^{2}+*kn* log(*n/k*))). The*k* best orthogonal spanning trees in the plane can be found in time*O*(*n* log*n*+*kn* log log(*n/k*)+*k*^{2}).

### C.R. categories

F.1.3 F.2.2 G.2.2 I.2.8## Copyright information

© BIT Foundations 1992