Generating Trees for Comparison

Generating functions for generating trees

Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the object. Generating trees lead to a fast computation of enumeration sequences (sometimes, to explicit formulae as well) and provide efficient random generation al...

Generating Better Decision Trees

A new decision tree learning algorithm called IDX is described. More general than existing algorithms, IDX addresses issues of decision tree quality largely overlooked in the artificial intelligence and machine learning literature. Decision tree size, error rate, and expected classification cost are just a few of the quality measures it can exploit. Furthermore, decision trees of varying qualit...

Generating Random Spanning Trees

This paper describes a probabilistic algorithm that, given a connected, undirected graph G with n vertices, produces a spanning tree of G chosen uniformly at random among the spanning trees of G. The expected running time is O(n logn) per generated tree for almost all graphs, and O(n3) for the worst graphs. Previously known deterministic algorithms and much more complicated and require O(n3) ti...

Generating Random Spanning Trees

Generating Colored Trees

A c-tree is a tree such that each vertex has a color c ∈ {c1, c2, · · · , cm}. In this paper we give a simple algorithm to generate all c-trees with at most n vertices and diameter d, without repetition. Our algorithm generates each c-tree in constant time. By using the algorithm for each diameter 2, 3, · · · , n− 1, we can generate all c-trees with n vertices.