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Linear Network Models

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Abstract

Six degrees of separation!

Keywords

  • Maxflow
  • Mincost
  • Shortest Path Model
  • Shortest Paths Variations
  • Flow Decision Variables

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-1-4842-3423-5_4
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Notes

  1. 1.

    www.oakland.edu/enp/

  2. 2.

    The first instance of such a model is usually attributed to Euler.

  3. 3.

    Note that there may be applications where the flow out of the source is to be maximized without regards to the flow in.

  4. 4.

    The theoretically-minded reader will research “total unimodularity.”

  5. 5.

    Bipartite means that there will never be any arcs between the top nodes or between the bottom nodes. You will see in the next section a more general problem.

  6. 6.

    If the reader reads American; a billion if English.

  7. 7.

    Note that if we can solve the longest path, we can solve the Hamiltonian path. Also, recall that linear programs can be solved in polynomial time. Ergo, if we can solve the longest path problem via LP, we prove P = NP. Then, we collect one million dollars from the Clay Mathematics Institute.

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© 2018 Serge Kruk

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Kruk, S. (2018). Linear Network Models. In: Practical Python AI Projects. Apress, Berkeley, CA. https://doi.org/10.1007/978-1-4842-3423-5_4

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