The.Algorithm.Design.Manual.Springer-Verlag.1998

Constructing All Paths in a Graph
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Constructing All Paths in a Graph
Enumerating all the simple paths from to t through a given graph is a somewhat more complicated
problem than listing permutations or subsets. Unlike the earlier problems, there is no explicit formula
that counts the number of solutions as a function of the number of edges or vertices, because the number
of paths depends upon the structure of the graph.
Figure: The search tree enumerating all simple paths from vertex 1 in the graph
Since the starting point of any path from to t is always , must be . The set of possible candidates for
the second position are the vertices v such that (,v) is an edge of the graph, for the path wanders from
vertex to vertex using edges to define the legal steps. In general, consists of the set of vertices
adjacent to that have not been used in the partial solution A. We can report a successful path whenever
. The solution vector A must have room for all n vertices, although most paths are likely to be
shorter than this. Figure shows the search tree giving all paths from a particular vertex in an example
graph.
Algorithms
Mon Jun 2 23:33:50 EDT 1997
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