Perfect sampling methods for random forests

<jats:p>A weighted graph<jats:italic>G</jats:italic>is a pair (<jats:italic>V</jats:italic>, ℰ) containing vertex set<jats:italic>V</jats:italic>and edge set ℰ, where each edge<jats:italic>e</jats:italic>∈ ℰ is associated with a weight<jats:italic>W<jats:sub>e</jats:sub></jats:italic>. A subgraph of<jats:italic>G</jats:italic>is a forest if it has no cycles. All forests on the graph<jats:italic>G</jats:italic>form a probability space, where the probability of each forest is proportional to the product of the weights of its edges. This paper aims to simulate forests exactly from the target distribution. Methods based on coupling from the past (CFTP) and rejection sampling are presented. Comparisons of these methods are given theoretically and via simulation.</jats:p>