Reverse search for enumeration Original Research Article

The reverse search technique has been recently introduced by the authors for efficient enumeration of vertices of polyhedra and arrangements. In this paper, we develop this idea in a general framework and show its broader applications to various problems in operations research, combinatorics, and geometry. In particular, we propose new algorithms for listing 1. (i) all triangulations of a set of n points in the plane. 2. (ii) all cells in a hyperplane arrangement in Rd, 3. (iii) all spanning trees of a graph, 4. (iv) all Euclidean (noncrossing) trees spanning a set of n points in the plane. 5. (v) all connected induced subgraphs of a graph, and 6. (vi) all topological orderings of an acyclic graph.