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We consider the problem of computing an $(s,d)$-hypernetwork in an acyclicF-hypergraph. This is a fundamental computational problem arising in directedhypergraphs, and is a foundational step in tackling problems of reachabilityand redundancy. This problem was previously explored in the context of generaldirected hypergraphs (containing cycles), where it is NP-hard, and acyclicB-hypergraphs, where a linear time algorithm can be achieved. In a surprisingcontrast, we find that for acyclic F-hypergraphs the problem is NP-hard, whichalso implies the problem is hard in BF-hypergraphs. This is a strikingcomplexity boundary given that F-hypergraphs and B-hypergraphs would at firstseem to be symmetrical to one another. We provide the proof of complexity andexplain why there is a fundamental asymmetry between the two classes ofdirected hypergraphs.

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