Maximal Independent Sets of a Hypergraph Alice Patrick
- Slides: 15
Maximal Independent Sets of a Hypergraph Alice & Patrick
What’s that then? A hypergraph G = (V, E) • V is a set of vertices • E is a set of hyperedges • an edge with 2 or more vertices An independent set S • assume vertices(e) is set of vertices in hyperedge e Maximal independent set S • there is no independent set S’ that subsumes S
A Hypergraph Show Me! 1 2 4 6 3 5 7 9 8
An Independent Set Show Me! 1 2 4 3 5 7 9 8 6 You could add vertex 3 or vertex 8! It aint maximal!
A Maximal Independent Set Show Me! 1 2 4 3 5 7 9 Now you’re talking! 8 6 There are 11 maximal independent sets of size 6
The Largest Independent Set Show Me! 1 2 4 3 5 7 6 There is only one for this graph 9 8
A Minimal Maximal Independent Set Show Me! 1 2 4 3 5 7 9 8 6 There are 3 minimal maximal independent set Honest!
… and now for a constraint programming solution … in Choco
CP/Choco 1 2 4 3 5 7 9 8 6 But what about maximality?
Encoding Maximality CP/Choco 1 2 4 3 5 7 9 8 6 An example, vertex 2 That is, we state when a variable MUST be selected and when it MUST NOT be selected
CP/Choco 1 2 4 5 3 9 7 8 6 Example, vertices 1, 2, and 3
More Generally
So?
Conclusion? • Is this any good? • What is state of the art? • Are there benchmark problems? • Is it new? It’s fun • In CP, I think so • Can we apply the encoding to other maximality problems? • I guess so. Care to suggest some? • Is it fun?
