We have a railway network with no cycles with expected profit at each station. Contractors bid for a subset of stations to maximize profit. A caterer may not bid for two adjacent stations. What is the best way to pick the stations?
For instance, here is a network:
10 20 \ / 30--------------40 / \ 20 30
In this case, the best choice are the outer four nodes with value 10+20+20+30 = 80.
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