TITLE: Edge Covering Shortest path
QUESTION [5 upvotes]: I have a graph of Points G(V,E) and I want to find the shortest path covering all the edge, I want the minimum number of edge repetitions .
Which is the best way to reduce this problem to well know problems like TSP , Hamiltonian circuit , Hamltonian completion ?
Thank you.

REPLY [5 votes]: That is Chinese Postman Path. Search for Chinese Postman Problem...
E.g., this section from some book looks comprehensive: http://ie454.cankaya.edu.tr/uploads/files/Chp-03%20044-064.pdf