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arXiv · 2201.04799

Finding $(s,d)$-Hypernetworks in F-Hypergraphs is NP-Hard

Reynaldo Gil-Pons·Max Ward·Loïc Miller
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Abstract

We consider the problem of computing an $(s,d)$-hypernetwork in an acyclic F-hypergraph. This is a fundamental computational problem arising in directed hypergraphs, and is a foundational step in tackling problems of reachability and redundancy. This problem was previously explored in the context of general directed hypergraphs (containing cycles), where it is NP-hard, and acyclic B-hypergraphs, where a linear time algorithm can be achieved. In a surprising contrast, we find that for acyclic F-hypergraphs the problem is NP-hard, which also implies the problem is hard in BF-hypergraphs. This is a striking complexity boundary given that F-hypergraphs and B-hypergraphs would at first seem to be symmetrical to one another. We provide the proof of complexity and explain why there is a fundamental asymmetry between the two classes of directed hypergraphs.

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Reynaldo Gil-Pons, Max Ward, Loïc Miller. 2022-01-13. Finding $(s,d)$-Hypernetworks in F-Hypergraphs is NP-Hard. https://arxiv.org/abs/2201.04799

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