Complexity of shortest B-hyperpaths with bounded tail size

Determine the computational complexity of finding a shortest B-hyperpath in a B-hypergraph when the cardinality of the tail E^- of every hyperedge is bounded by a constant K, and in particular when K = 2; ascertain whether the problem remains NP-hard or admits a polynomial-time algorithm under these tail-size constraints.

Background

In the paper, assembly pathways in the sense of assembly theory are shown to coincide with minimal B-hyperpaths in B-hypergraphs. It is known that finding a shortest B-hyperpath is NP-hard in general.

However, assembly spaces naturally correspond to B-hypergraphs with tails of cardinality 2 (i.e., |E^-| = 2), motivating the question whether restricting the tail size to a fixed constant K—especially K = 2—changes the computational complexity of the shortest B-hyperpath problem. Clarifying this would directly impact the computational tractability of assembly-pathway computation in assembly theory.