dwave_networkx.algorithms.matching.min_maximal_matching

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

Returns an approximate minimal maximal matching.

Defines a QUBO with ground states corresponding to a minimal maximal matching and uses the sampler to sample from it.

A matching is a subset of edges in which no node occurs more than once. A maximal matching is one in which no edges from G can be added without violating the matching rule. A minimal maximal matching is the smallest maximal matching for G.

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:

matching – A minimal maximal matching of the graph.
Return type:

set

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/Matching_(graph_theory)

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.