When doing Nearest Neighbor Algorithm, you might get different circuits depending on which vertex you start at$.$ A variation on the Nearest Neighbor Algorithm for finding the shortest Hamilton circuit is called the "Repeated Nearest Neighbor Algorithm" $($RNNA$).$ To do RNNA on a graph with

vertices, you do Nearest Neighbor Algorithm

times$--$once starting at each vertex. You then select the circuit among the

circuits you found with the smallest total weight. See the textbook pages $136-138$ for more details.

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