# dwave_networkx.algorithms.elimination_ordering.min_fill_heuristic¶

min_fill_heuristic(G)[source]

Computes an upper bound on the treewidth of graph G based on the min-fill heuristic for the elimination ordering.

Parameters

G (NetworkX graph) – The graph on which to compute an upper bound for the treewidth.

Returns

• treewidth_upper_bound (int) – An upper bound on the treewidth of the graph G.

• order (list) – An elimination order that induces the treewidth.

Examples

This example computes an upper bound for the treewidth of the $$K_4$$ complete graph.

>>> K_4 = nx.complete_graph(4)
>>> tw, order = dnx.min_fill_heuristic(K_4)


References

Based on the algorithm presented in [GD]