# Generalized max-flows and min-cuts in simplicial complexes

@inproceedings{Maxwell2021GeneralizedMA, title={Generalized max-flows and min-cuts in simplicial complexes}, author={William Maxwell and Amir Nayyeri}, booktitle={ESA}, year={2021} }

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…

## 3 Citations

### The complexity of high-dimensional cuts

- Mathematics, Computer ScienceArXiv
- 2021

The algorithmic study of some cut problems in high dimensions, namely, Topological Hitting Set and Boundary Nontrivialization, and randomized (approximation) FPT algorithms for the global variants of THS and BNT are initiated.

### Effective Resistance and Capacitance in Simplicial Complexes and a Quantum Algorithm

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- 2021

We investigate generalizations of the graph theoretic notions of effective resistance and capacitance to simplicial complexes and prove analogs of formulas known in the case of graphs. In graphs the…

### Hardness Results for Laplacians of Simplicial Complexes via Sparse-Linear Equation Complete Gadgets

- MathematicsICALP
- 2022

We study linear equations in combinatorial Laplacians of k -dimensional simplicial complexes ( k -complexes), a natural generalization of graph Laplacians. Combinatorial Laplacians play a crucial…

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