Since the Euclidean TSP is also NP-hard, approximation algorithms have been developed to solve it. A popular approximate solution is the 2-approximation double minimum spanning tree algorithm.

Pseudo code:
1. Build a minimal spanning tree (MST) from the set of all cities.
2. Duplicate all edges, we can now easily construct an Euler cycle.
3. Traverse the cycle, but do not visit any node more than once, taking shortcuts when a node has been visited.