# Eulerian Cycle/Chinese Postman

 Input Output

Input Description: A graph $$G=(V,E)$$.}
Problem: Find the shortest tour of $$G$$ visiting each edge at least once.

Excerpt from The Algorithm Design Manual: Suppose you are given the map of a city and charged with designing the routes for garbage trucks, snow plows, or postmen. In all of these applications, every road in the city must be completely traversed at least once in order to ensure that all deliveries or pickups are made. For efficiency, you seek to minimize total drive time, or equivalently, the total distance or number of edges traversed.

Such applications are variants of the Eulerian cycle problem, best characterized by the children's puzzle that asks them to draw a given figure completely without lifting their pencil off the paper and without repeating any edges. We seek a path or cycle through a graph that visits each edge exactly once.

### Related Problems

 Hamiltonian Cycle Matching

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