dwave_networkx.algorithms.cover.min_vertex_cover

min_vertex_cover(G, sampler=None, **sampler_args)[source]

Returns an approximate minimum vertex cover.

Defines a QUBO with ground states corresponding to a minimum vertex cover and uses the sampler to sample from it.

A vertex cover is a set of vertices such that each edge of the graph is incident with at least one vertex in the set. A minimum vertex cover is the vertex cover of smallest size.

Parameters:
  • G (NetworkX graph) –
  • sampler – A binary quadratic model sampler. A sampler is a process that samples from low energy states in models defined by an Ising equation or a Quadratic Unconstrained Binary Optimization Problem (QUBO). A sampler is expected to have a ‘sample_qubo’ and ‘sample_ising’ method. A sampler is expected to return an iterable of samples, in order of increasing energy. If no sampler is provided, one must be provided using the set_default_sampler function.
  • sampler_args – Additional keyword parameters are passed to the sampler.
Returns:

vertex_cover – List of nodes that the form a the minimum vertex cover, as determined by the given sampler.
Return type:

list

Examples

>>> G = dnx.chimera_graph(1, 2, 3)
>>> dnx.min_vertex_cover(G, sampler)
[0, 1, 2, 9, 10, 11]

Notes

Samplers by their nature may not return the optimal solution. This function does not attempt to confirm the quality of the returned sample.

https://en.wikipedia.org/wiki/Vertex_cover

https://en.wikipedia.org/wiki/Quadratic_unconstrained_binary_optimization

References

[AL]Lucas, A. (2014). Ising formulations of many NP problems. Frontiers in Physics, Volume 2, Article 5.