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A hill climbing algorithm doesn't make any sense to me for a dependency graph, it doesn't fit the domain at all.

Is there a canonical reference you'd recommend to understand this problem or a paper I could look at that was similar to this implementation?

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Sometimes discrete graph theory problems can be relaxed into a continuous space where gradient descent can be used. If you want a concrete example of how this happens, take a look at the "Continuous Optimization" section in the "Thirty Years of Graph Matching in Pattern Recognition" paper (graph/subgraph isomorphism).

Thank you, I will investigate this.

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