On the dualization in distributive lattices and related problems

In this paper, we study the dualization in distributive lattices, a generalization of well-known hypergraph problem. We particular propose equivalent formulations problem terms graphs, hypergraphs, and posets. It is known that amounts to generate all minimal transversals hypergraph, or dominating sets graph. new framework, poset on vertices given together with input (hyper)graph, “ideal solutions” are be generated. This allows us complexity under various combined restrictions graph classes types, including bipartite, split, co-bipartite variants neighborhood inclusion For example, show while enumeration possible linear delay split problem, within same class, gets as hard for general graphs when generalized framework. More surprisingly, result holds even only comparing included neighborhoods If both class sufficiently restricted, tractable relying existing algorithms from literature.