A similar algorithm can also enumerate all bases of a linear program, without requiring that it defines a polytope that is simple. Applying reverse search to this data generates all vertices of the polytope. Any such pivot rule can be interpreted as defining the parent function of a spanning tree of the polytope, whose root is the optimal vertex. The simplex algorithm from the theory of linear programming finds a vertex maximizing a given linear function of the coordinates, by walking from vertex to vertex, choosing at each step a vertex with a greater value of the function there are several standard choices of "pivot rule" that specify more precisely which vertex to choose. This algorithm involves listing the neighbors of an object once for each step in the search. In the remaining case, when there is no next child and the current object is the root, the reverse search terminates. If there is no next child and the current object is not the root, the next object is the parent of the current object. If another child is found in this way, it is the next object. The algorithm lists the children (that is, state-space neighbors of the current object that have the current object as their parent) one at a time until reaching this previous child, and then takes one more step in this list of children.
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