Section 2: Route inspection problems Key point 2.8 A route is like a cycle or closed trail except that edges can be repeated.
Rewind You found cycles and trails in Chapter 1.
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Key point 2.9 A route inspection problem involves finding a least weight route that uses every arc of a network.
The problem was originally studied by the Chinese mathematician Kwan Mei-Ko in 1960, and is also known as the Chinese postman problem.
Key point 2.10
Any network formed by weighting an Eulerian graph can be traversed without having to repeat any arcs.
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Otherwise, arcs need to be doubled up, in the way that uses the least weight possible, so that the graph that was weighted to form the network becomes Eulerian.
WORKED EXAMPLE 2.7
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Solve the Chinese postman (route inspection) problem for this network.
The odddegree nodes
The solution needs all nodes of even degree.
are D and H . The least weight path connecting D to H is
In this case there is just one pair of odd nodes so this is the minimum total weight to be added to make all nodes of even degree.
D − E − H = 7
75 + 7 = 82
Total weight of original graph =
75
. This would often be given in the question.
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