Finding Minimal Spanning Forests in a Grap.

propose two algorithms for solving a graph partitioning problem motivated by computational topology. Specifically, given a weighted, undirected graph $G$ and a positive integer $k$, we desire to find $k$ disjoint trees within $G$ such that each vertex of $G$ is contained in one of the trees and the weight of largest tree is as small as possible. are unable to find this problem in the graph partitioning literature, but we show that the problem is NP-complete. We propose two approximation algorithms, one that uses a spectral clustering approach and another that employs a dynamic programming strategy, that produce near-optimal partitions on a family of test graphs. describe these algorithms and analyze their empirical performance.