Generalized max-flows and min-cuts in simplicial complexes

  title={Generalized max-flows and min-cuts in simplicial complexes},
  author={William Maxwell and Amir Nayyeri},
We consider high dimensional variants of the maximum flow and minimum cut problems in the setting of simplicial complexes and provide both algorithmic and hardness results. By viewing flows and cuts topologically in terms of the simplicial (co)boundary operator we can state these problems as linear programs and show that they are dual to one another. Unlike graphs, complexes with integral capacity constraints may have fractional max-flows. We show that computing a maximum integral flow is NP… 
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