Constant Time Generation of Free Trees

An algorithm of Beyer and Hedetniemi for generating unlabeled rooted trees is extended to generate unlabeled free trees. Abstract An algorithm of Beyer and Hedetniemi for generating unlabeled rooted trees is extended to generate unlabeled free trees. “The Beyer-Hedetniemi technique is refined to produce only one member of each equivalence class of rooted trees under isomorphism of the underlying free (unrooted) trees.”An algorithm of Beyer and Hedetniemi for generating unlabeled rooted trees is extended to generate unlabeled free trees. “The Beyer-Hedetniemi technique is refined to produce only one member of each equivalence class of rooted trees under isomorphism of the underlying free (unrooted) trees.” Beyer-Hedetniemi Algorithm generating rooted trees Beyer-Hedetniemi Algorithm generating rooted trees Basics Represent rooted tree using a sequence Use an iterative procedure (successor function) to generate all sequences (“The method uses a successor function to traverse an ordered set of integer sequences which represents the objects being generated”). Rooted Tree Representation with Sequences Pre-order traversal with distance from root 1 2 3 4 4 3 2 2 3 4 3 2 3 4 4 2 2 3 3 4 3 Rooted Tree Representation with Sequences Pre-order traversal with distance from root 1 2 3 4 4 3 2 2 3 4 3 2 3 4 4 2 2 3 3 4 3