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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.

flag	asked Jul 17 2011 at 9:37 Denis 43●3

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Well, all you need is to take care of vertices of odd degree: you have to split all of them but 2 into pairs and joint the pairs so that the total length is minimal. That is exactly the optimal matching problem, which certainly belongs to the category of "well-known". – fedja Jul 17 2011 at 12:05

Thank you for your suggestion – Denis Jul 18 2011 at 8:21

Max Alekseyev · Accepted Answer · 2011-07-17 20:27:27Z UTC

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That is Chinese Postman Path. Search for Chinese Postman Problem...

E.g., this section from some book looks comprehensive: http://academic.cankaya.edu.tr/~kandiller/eski_ie454/Chp-03%20044-064.pdf

edited Jul 17 2011 at 20:27

answered Jul 17 2011 at 20:14

Max Alekseyev
1,751●4●9

Thank you for the solution – Denis Jul 18 2011 at 8:21

Edge Covering Shortest path

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