Decision Trees and Diagrams

Abstract

Decision trees and diagrams (also known as sequential evaluation procedures) have widespread applications in databases, dec~smn table programming, concrete complexity theory, switching theory, pattern recognmon, and taxonomy--in short, wherever discrete functions must be evaluated sequentially. In this tutorial survey a common framework of defimtmns and notation is established, the contributions from the main fields of apphcatmn are reviewed, recent results and extensions are presented, and areas of ongoing and future research are discussed.

Algorithms for optimal dyadic decision trees

“…The evolution of decision tree design methods can be traced through a collection of survey articles that span nearly four decades of work (Pooch 1974;Moret 1982;Safavian and Landgrebe 1991;Murthy 1998). Decision tree design problems are roughly characterized by the following ingredients:…”

Forward and inverse transformations between Haar spectra and ordered binary decision diagrams of Boolean functions

“…A Binary Decision Diagram (BDD) [2], [3], [5], [10], [18], [19], [21], [23], [24] is a Rooted Directed Acyclic Graph representation with Node (or Vertex) Set V and Edge Set E. The Node Set consists of two types of nodes: the nonterminal and terminal nodes. A nonterminal node v ∈ V has as attributes an index, denoted by index(v), to identify an input variable of a function, and two children (or successors), low(v) and high(v) ∈ V. A terminal node u ∈ V has no child, and it has a value, denoted by value(u).…”

Untitled

“…For a comprehensive discussion of decision trees, see Moret [1982] and Breiman, Friedman, Olshen, and Stone [1984].…”