1. Complexity Dichotomies for the Minimum $$\mathcal {F}$$-Overlay Problem
- Author
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Dorian Mazauric, Rémi Watrigant, Nathann Cohen, Ignasi Sau, and Frédéric Havet
- Subjects
Combinatorics ,Hypergraph ,Spanning subgraph ,010201 computation theory & mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Complete graph ,020206 networking & telecommunications ,0102 computer and information sciences ,02 engineering and technology ,Overlay ,01 natural sciences ,Graph ,Mathematics - Abstract
For a (possibly infinite) fixed family of graphs \(\mathcal {F}\), we say that a graph G overlays \(\mathcal {F}\) on a hypergraph H if V(H) is equal to V(G) and the subgraph of G induced by every hyperedge of H contains some member of \(\mathcal {F}\) as a spanning subgraph. While it is easy to see that the complete graph on |V(H)| overlays \(\mathcal {F}\) on a hypergraph H whenever the problem admits a solution, the Minimum \(\mathcal {F}\)-Overlay problem asks for such a graph with the minimum number of edges. This problem allows to generalize some natural problems which may arise in practice. For instance, if the family \(\mathcal {F}\) contains all connected graphs, then Minimum \(\mathcal {F}\)-Overlay corresponds to the Minimum Connectivity Inference problem (also known as Subset Interconnection Design problem) introduced for the low-resolution reconstruction of macro-molecular assembly in structural biology, or for the design of networks.
- Published
- 2018
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