The Steiner problem in graphs

SE Dreyfus, RA Wagner - Networks, 1971 - Wiley Online Library
SE Dreyfus, RA Wagner
Networks, 1971Wiley Online Library
An algorithm for solving the Steiner problem on a finite undirected graph is presented. This
algorithm computes the set of graph arcs of minimum total length needed to connect a
specified set of k graph nodes. If the entire graph contains n nodes, the algorithm requires
time proportional to n3/2+ n2 (2k‐1‐k‐1)+ n (3k‐1‐2k+ 3)/2. The time requirement above
includes the term n3/2, which can be eliminated if the set of shortest paths connecting each
pair of nodes in the graph is available.
Abstract
An algorithm for solving the Steiner problem on a finite undirected graph is presented. This algorithm computes the set of graph arcs of minimum total length needed to connect a specified set of k graph nodes. If the entire graph contains n nodes, the algorithm requires time proportional to n3/2 + n2 (2k‐1 ‐ k ‐ 1) + n(3k‐1 ‐ 2k + 3)/2.
The time requirement above includes the term n3/2, which can be eliminated if the set of shortest paths connecting each pair of nodes in the graph is available.
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