Shortest path to visit all nodes in a complete directed graph

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Note: This is almost the same questions as this: Shortest path to visit all nodes

But I have a complete graph.

Problem: Consider a complete undirected graph with nonnegative edge lengths. Question: Compute the shortest path that visits every node at least once.

NB: This is NOT the TSP problem. The path does not have an ending node and the path can pass through nodes more than once.

Other notes:

The number of nodes is small (less than 20).

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