Reverse Search; Enumeration Algorithms

Years and Authors of Summarized Original Work

• 1996; Avis, Fukuda

• 2003; Uno

• 2004; Nakano, Uno

Problem Definition

We will consider enumeration problems, i.e., we want to list all the objects that satisfy given conditions (e.g., vertices of a polytope $\{\boldsymbol{x}\ \vert \ A\boldsymbol{x} \geq \boldsymbol{ b}\}$ or maximal cliques in a given graph). One object should not be listed twice or more.

Introduction

In this entry, we consider an enumeration scheme called reverse search developed by Avis and Fukuda [1]. The scheme was originally developed to enumerate all the vertices of a given polytope represented by the intersection of half spaces [1]. The scheme is very powerful, and quite many kinds of objects such as arrangements in a hyperplane, triangulations of a polygon, bases of a matroid, spanning trees, trees, or maximal cliques in a graph, plane graphs of given number of vertices, etc., can be enumerated with it [1–4, 6].

Think of a problem to enumerate (or visit) all the...