U :v f@sbdZddlmZddlmZddlZddlmZddgZ dd dZ dd dZ dd d Z d dZ dS)zB Cuthill-McKee ordering of graph nodes to produce sparse matrices )deque) itemgetterN)arbitrary_elementcuthill_mckee_orderingreverse_cuthill_mckee_orderingccs*t|D]}t|||EdHq dS)aGenerate an ordering (permutation) of the graph nodes to make a sparse matrix. Uses the Cuthill-McKee heuristic (based on breadth-first search) [1]_. Parameters ---------- G : graph A NetworkX graph heuristic : function, optional Function to choose starting node for RCM algorithm. If None a node from a pseudo-peripheral pair is used. A user-defined function can be supplied that takes a graph object and returns a single node. Returns ------- nodes : generator Generator of nodes in Cuthill-McKee ordering. Examples -------- >>> from networkx.utils import cuthill_mckee_ordering >>> G = nx.path_graph(4) >>> rcm = list(cuthill_mckee_ordering(G)) >>> A = nx.adjacency_matrix(G, nodelist=rcm) Smallest degree node as heuristic function: >>> def smallest_degree(G): ... return min(G, key=G.degree) >>> rcm = list(cuthill_mckee_ordering(G, heuristic=smallest_degree)) See Also -------- reverse_cuthill_mckee_ordering Notes ----- The optimal solution the bandwidth reduction is NP-complete [2]_. References ---------- .. [1] E. Cuthill and J. McKee. Reducing the bandwidth of sparse symmetric matrices, In Proc. 24th Nat. Conf. ACM, pages 157-172, 1969. http://doi.acm.org/10.1145/800195.805928 .. [2] Steven S. Skiena. 1997. The Algorithm Design Manual. Springer-Verlag New York, Inc., New York, NY, USA. N)nxZconnected_components connected_cuthill_mckee_orderingZsubgraph)G heuristiccr 6/tmp/pip-unpacked-wheel-_lngutwb/networkx/utils/rcm.pyrs5cCsttt||dS)aGenerate an ordering (permutation) of the graph nodes to make a sparse matrix. Uses the reverse Cuthill-McKee heuristic (based on breadth-first search) [1]_. Parameters ---------- G : graph A NetworkX graph heuristic : function, optional Function to choose starting node for RCM algorithm. If None a node from a pseudo-peripheral pair is used. A user-defined function can be supplied that takes a graph object and returns a single node. Returns ------- nodes : generator Generator of nodes in reverse Cuthill-McKee ordering. Examples -------- >>> from networkx.utils import reverse_cuthill_mckee_ordering >>> G = nx.path_graph(4) >>> rcm = list(reverse_cuthill_mckee_ordering(G)) >>> A = nx.adjacency_matrix(G, nodelist=rcm) Smallest degree node as heuristic function: >>> def smallest_degree(G): ... return min(G, key=G.degree) >>> rcm = list(reverse_cuthill_mckee_ordering(G, heuristic=smallest_degree)) See Also -------- cuthill_mckee_ordering Notes ----- The optimal solution the bandwidth reduction is NP-complete [2]_. References ---------- .. [1] E. Cuthill and J. McKee. Reducing the bandwidth of sparse symmetric matrices, In Proc. 24th Nat. Conf. ACM, pages 157-72, 1969. http://doi.acm.org/10.1145/800195.805928 .. [2] Steven S. Skiena. 1997. The Algorithm Design Manual. Springer-Verlag New York, Inc., New York, NY, USA. )r )reversedlistr)r r r r rrGs5ccs|dkrt|}n||}|h}t|g}|r|}|Vt|t|||tdd}dd|D}||||q*dS)NkeycSsg|] \}}|qSr r ).0ndr r r sz4connected_cuthill_mckee_ordering..) pseudo_peripheral_noderpopleftsorteddegreesetrupdateextend)r r startvisitedqueueparentZndchildrenr r rr s  " r cspt|}d}|}tt||}t||kr6ql}fdd|D}t||t dd\}}q|S)Nrc3s|]\}}|kr|VqdS)Nr )rrdistlr r sz)pseudo_peripheral_node..rr) rdictrZshortest_path_lengthmaxvaluesitemsminrr)r ulpvZsplZfarthestdegr r%rrs r)N)N)N)__doc__ collectionsroperatorrZnetworkxrutilsr__all__rrr rr r r rs    9 8