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Reverse search for enumeration. (English) Zbl 0854.68070
Summary: 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 (i) all triangulations of a set of $$n$$ points in the plane, (ii) all cells in a hyperplane arrangement in $$R^d$$, (iii) all spanning trees of a graph, (iv) all Euclidean (noncrossing) trees spanning a set of $$n$$ points in the plane, (v) all connected induced subgraphs of a graph, and (vi) all topological orderings of an acyclic graph. Finally, we propose a new algorithm for the 0-1 integer programming problem which can be considered as an alternative to the branch-and-bound algorithm.

##### MSC:
 68R10 Graph theory (including graph drawing) in computer science 05C30 Enumeration in graph theory 05C05 Trees
##### Keywords:
reverse search technique
##### Software:
Mathematica; VertexEnumeration; PWTri
Full Text:
##### References:
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