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arXiv · 1902.02404

Flow-firing processes

Pedro Felzenszwalb·Caroline Klivans
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Abstract

We consider a discrete non-deterministic flow-firing process for rerouting flow on the edges of a planar complex. The process is an instance of higher-dimensional chip-firing. In the flow-firing process, flow on the edges of a complex is repeatedly diverted across the faces of the complex. For non-conservative initial configurations we show this process never terminates. For conservative initial flows we show the process terminates after a finite number of rerouting steps, but there are many possible final configurations reachable from a single initial state. Finally, for conservative initial flows around a topological hole we show the process terminates at a unique final configuration. In this case the process exhibits global confluence despite not satisfying local confluence.

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Pedro Felzenszwalb, Caroline Klivans. 2019-02-06. Flow-firing processes. https://arxiv.org/abs/1902.02404

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