# -*- coding: utf-8 -*- # Copyright (C) 2010 by # Aric Hagberg # Dan Schult # Pieter Swart # All rights reserved. # BSD license. # # Author: Andrey Paramonov """ Functions measuring similarity using graph edit distance. The graph edit distance is the number of edge/node changes needed to make two graphs isomorphic. The default algorithm/implementation is sub-optimal for some graphs. The problem of finding the exact Graph Edit Distance (GED) is NP-hard so it is often slow. If the simple interface `graph_edit_distance` takes too long for your graph, try `optimize_graph_edit_distance` and/or `optimize_edit_paths`. At the same time, I encourage capable people to investigate alternative GED algorithms, in order to improve the choices available. """ from __future__ import print_function import math import networkx as nx from operator import * import sys __author__ = 'Andrey Paramonov ' __all__ = [ 'graph_edit_distance', 'optimal_edit_paths', 'optimize_graph_edit_distance', 'optimize_edit_paths' ] def debug_print(*args, **kwargs): print(*args, **kwargs) def graph_edit_distance(G1, G2, node_match=None, edge_match=None, node_subst_cost=None, node_del_cost=None, node_ins_cost=None, edge_subst_cost=None, edge_del_cost=None, edge_ins_cost=None, upper_bound=None): """Returns GED (graph edit distance) between graphs G1 and G2. Graph edit distance is a graph similarity measure analogous to Levenshtein distance for strings. It is defined as minimum cost of edit path (sequence of node and edge edit operations) transforming graph G1 to graph isomorphic to G2. Parameters ---------- G1, G2: graphs The two graphs G1 and G2 must be of the same type. node_match : callable A function that returns True if node n1 in G1 and n2 in G2 should be considered equal during matching. The function will be called like node_match(G1.nodes[n1], G2.nodes[n2]). That is, the function will receive the node attribute dictionaries for n1 and n2 as inputs. Ignored if node_subst_cost is specified. If neither node_match nor node_subst_cost are specified then node attributes are not considered. edge_match : callable A function that returns True if the edge attribute dictionaries for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should be considered equal during matching. The function will be called like edge_match(G1[u1][v1], G2[u2][v2]). That is, the function will receive the edge attribute dictionaries of the edges under consideration. Ignored if edge_subst_cost is specified. If neither edge_match nor edge_subst_cost are specified then edge attributes are not considered. node_subst_cost, node_del_cost, node_ins_cost : callable Functions that return the costs of node substitution, node deletion, and node insertion, respectively. The functions will be called like node_subst_cost(G1.nodes[n1], G2.nodes[n2]), node_del_cost(G1.nodes[n1]), node_ins_cost(G2.nodes[n2]). That is, the functions will receive the node attribute dictionaries as inputs. The functions are expected to return positive numeric values. Function node_subst_cost overrides node_match if specified. If neither node_match nor node_subst_cost are specified then default node substitution cost of 0 is used (node attributes are not considered during matching). If node_del_cost is not specified then default node deletion cost of 1 is used. If node_ins_cost is not specified then default node insertion cost of 1 is used. edge_subst_cost, edge_del_cost, edge_ins_cost : callable Functions that return the costs of edge substitution, edge deletion, and edge insertion, respectively. The functions will be called like edge_subst_cost(G1[u1][v1], G2[u2][v2]), edge_del_cost(G1[u1][v1]), edge_ins_cost(G2[u2][v2]). That is, the functions will receive the edge attribute dictionaries as inputs. The functions are expected to return positive numeric values. Function edge_subst_cost overrides edge_match if specified. If neither edge_match nor edge_subst_cost are specified then default edge substitution cost of 0 is used (edge attributes are not considered during matching). If edge_del_cost is not specified then default edge deletion cost of 1 is used. If edge_ins_cost is not specified then default edge insertion cost of 1 is used. upper_bound : numeric Maximum edit distance to consider. Return None if no edit distance under or equal to upper_bound exists. Examples -------- >>> G1 = nx.cycle_graph(6) >>> G2 = nx.wheel_graph(7) >>> nx.graph_edit_distance(G1, G2) 7.0 See Also -------- optimal_edit_paths, optimize_graph_edit_distance, is_isomorphic (test for graph edit distance of 0) References ---------- .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick Martineau. An Exact Graph Edit Distance Algorithm for Solving Pattern Recognition Problems. 4th International Conference on Pattern Recognition Applications and Methods 2015, Jan 2015, Lisbon, Portugal. 2015, <10.5220/0005209202710278>. https://hal.archives-ouvertes.fr/hal-01168816 """ bestcost = None for vertex_path, edge_path, cost in \ optimize_edit_paths(G1, G2, node_match, edge_match, node_subst_cost, node_del_cost, node_ins_cost, edge_subst_cost, edge_del_cost, edge_ins_cost, upper_bound, True): #assert bestcost is None or cost < bestcost bestcost = cost return bestcost def optimal_edit_paths(G1, G2, node_match=None, edge_match=None, node_subst_cost=None, node_del_cost=None, node_ins_cost=None, edge_subst_cost=None, edge_del_cost=None, edge_ins_cost=None, upper_bound=None): """Returns all minimum-cost edit paths transforming G1 to G2. Graph edit path is a sequence of node and edge edit operations transforming graph G1 to graph isomorphic to G2. Edit operations include substitutions, deletions, and insertions. Parameters ---------- G1, G2: graphs The two graphs G1 and G2 must be of the same type. node_match : callable A function that returns True if node n1 in G1 and n2 in G2 should be considered equal during matching. The function will be called like node_match(G1.nodes[n1], G2.nodes[n2]). That is, the function will receive the node attribute dictionaries for n1 and n2 as inputs. Ignored if node_subst_cost is specified. If neither node_match nor node_subst_cost are specified then node attributes are not considered. edge_match : callable A function that returns True if the edge attribute dictionaries for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should be considered equal during matching. The function will be called like edge_match(G1[u1][v1], G2[u2][v2]). That is, the function will receive the edge attribute dictionaries of the edges under consideration. Ignored if edge_subst_cost is specified. If neither edge_match nor edge_subst_cost are specified then edge attributes are not considered. node_subst_cost, node_del_cost, node_ins_cost : callable Functions that return the costs of node substitution, node deletion, and node insertion, respectively. The functions will be called like node_subst_cost(G1.nodes[n1], G2.nodes[n2]), node_del_cost(G1.nodes[n1]), node_ins_cost(G2.nodes[n2]). That is, the functions will receive the node attribute dictionaries as inputs. The functions are expected to return positive numeric values. Function node_subst_cost overrides node_match if specified. If neither node_match nor node_subst_cost are specified then default node substitution cost of 0 is used (node attributes are not considered during matching). If node_del_cost is not specified then default node deletion cost of 1 is used. If node_ins_cost is not specified then default node insertion cost of 1 is used. edge_subst_cost, edge_del_cost, edge_ins_cost : callable Functions that return the costs of edge substitution, edge deletion, and edge insertion, respectively. The functions will be called like edge_subst_cost(G1[u1][v1], G2[u2][v2]), edge_del_cost(G1[u1][v1]), edge_ins_cost(G2[u2][v2]). That is, the functions will receive the edge attribute dictionaries as inputs. The functions are expected to return positive numeric values. Function edge_subst_cost overrides edge_match if specified. If neither edge_match nor edge_subst_cost are specified then default edge substitution cost of 0 is used (edge attributes are not considered during matching). If edge_del_cost is not specified then default edge deletion cost of 1 is used. If edge_ins_cost is not specified then default edge insertion cost of 1 is used. upper_bound : numeric Maximum edit distance to consider. Returns ------- edit_paths : list of tuples (node_edit_path, edge_edit_path) node_edit_path : list of tuples (u, v) edge_edit_path : list of tuples ((u1, v1), (u2, v2)) cost : numeric Optimal edit path cost (graph edit distance). Examples -------- >>> G1 = nx.cycle_graph(6) >>> G2 = nx.wheel_graph(7) >>> paths, cost = nx.optimal_edit_paths(G1, G2) >>> len(paths) 84 >>> cost 7.0 See Also -------- graph_edit_distance, optimize_edit_paths References ---------- .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick Martineau. An Exact Graph Edit Distance Algorithm for Solving Pattern Recognition Problems. 4th International Conference on Pattern Recognition Applications and Methods 2015, Jan 2015, Lisbon, Portugal. 2015, <10.5220/0005209202710278>. https://hal.archives-ouvertes.fr/hal-01168816 """ paths = list() bestcost = None for vertex_path, edge_path, cost in \ optimize_edit_paths(G1, G2, node_match, edge_match, node_subst_cost, node_del_cost, node_ins_cost, edge_subst_cost, edge_del_cost, edge_ins_cost, upper_bound, False): #assert bestcost is None or cost <= bestcost if bestcost is not None and cost < bestcost: paths = list() paths.append((vertex_path, edge_path)) bestcost = cost return paths, bestcost def optimize_graph_edit_distance(G1, G2, node_match=None, edge_match=None, node_subst_cost=None, node_del_cost=None, node_ins_cost=None, edge_subst_cost=None, edge_del_cost=None, edge_ins_cost=None, upper_bound=None): """Returns consecutive approximations of GED (graph edit distance) between graphs G1 and G2. Graph edit distance is a graph similarity measure analogous to Levenshtein distance for strings. It is defined as minimum cost of edit path (sequence of node and edge edit operations) transforming graph G1 to graph isomorphic to G2. Parameters ---------- G1, G2: graphs The two graphs G1 and G2 must be of the same type. node_match : callable A function that returns True if node n1 in G1 and n2 in G2 should be considered equal during matching. The function will be called like node_match(G1.nodes[n1], G2.nodes[n2]). That is, the function will receive the node attribute dictionaries for n1 and n2 as inputs. Ignored if node_subst_cost is specified. If neither node_match nor node_subst_cost are specified then node attributes are not considered. edge_match : callable A function that returns True if the edge attribute dictionaries for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should be considered equal during matching. The function will be called like edge_match(G1[u1][v1], G2[u2][v2]). That is, the function will receive the edge attribute dictionaries of the edges under consideration. Ignored if edge_subst_cost is specified. If neither edge_match nor edge_subst_cost are specified then edge attributes are not considered. node_subst_cost, node_del_cost, node_ins_cost : callable Functions that return the costs of node substitution, node deletion, and node insertion, respectively. The functions will be called like node_subst_cost(G1.nodes[n1], G2.nodes[n2]), node_del_cost(G1.nodes[n1]), node_ins_cost(G2.nodes[n2]). That is, the functions will receive the node attribute dictionaries as inputs. The functions are expected to return positive numeric values. Function node_subst_cost overrides node_match if specified. If neither node_match nor node_subst_cost are specified then default node substitution cost of 0 is used (node attributes are not considered during matching). If node_del_cost is not specified then default node deletion cost of 1 is used. If node_ins_cost is not specified then default node insertion cost of 1 is used. edge_subst_cost, edge_del_cost, edge_ins_cost : callable Functions that return the costs of edge substitution, edge deletion, and edge insertion, respectively. The functions will be called like edge_subst_cost(G1[u1][v1], G2[u2][v2]), edge_del_cost(G1[u1][v1]), edge_ins_cost(G2[u2][v2]). That is, the functions will receive the edge attribute dictionaries as inputs. The functions are expected to return positive numeric values. Function edge_subst_cost overrides edge_match if specified. If neither edge_match nor edge_subst_cost are specified then default edge substitution cost of 0 is used (edge attributes are not considered during matching). If edge_del_cost is not specified then default edge deletion cost of 1 is used. If edge_ins_cost is not specified then default edge insertion cost of 1 is used. upper_bound : numeric Maximum edit distance to consider. Returns ------- Generator of consecutive approximations of graph edit distance. Examples -------- >>> G1 = nx.cycle_graph(6) >>> G2 = nx.wheel_graph(7) >>> for v in nx.optimize_graph_edit_distance(G1, G2): ... minv = v >>> minv 7.0 See Also -------- graph_edit_distance, optimize_edit_paths References ---------- .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick Martineau. An Exact Graph Edit Distance Algorithm for Solving Pattern Recognition Problems. 4th International Conference on Pattern Recognition Applications and Methods 2015, Jan 2015, Lisbon, Portugal. 2015, <10.5220/0005209202710278>. https://hal.archives-ouvertes.fr/hal-01168816 """ for vertex_path, edge_path, cost in \ optimize_edit_paths(G1, G2, node_match, edge_match, node_subst_cost, node_del_cost, node_ins_cost, edge_subst_cost, edge_del_cost, edge_ins_cost, upper_bound, True): yield cost def optimize_edit_paths(G1, G2, node_match=None, edge_match=None, node_subst_cost=None, node_del_cost=None, node_ins_cost=None, edge_subst_cost=None, edge_del_cost=None, edge_ins_cost=None, upper_bound=None, strictly_decreasing=True): """GED (graph edit distance) calculation: advanced interface. Graph edit path is a sequence of node and edge edit operations transforming graph G1 to graph isomorphic to G2. Edit operations include substitutions, deletions, and insertions. Graph edit distance is defined as minimum cost of edit path. Parameters ---------- G1, G2: graphs The two graphs G1 and G2 must be of the same type. node_match : callable A function that returns True if node n1 in G1 and n2 in G2 should be considered equal during matching. The function will be called like node_match(G1.nodes[n1], G2.nodes[n2]). That is, the function will receive the node attribute dictionaries for n1 and n2 as inputs. Ignored if node_subst_cost is specified. If neither node_match nor node_subst_cost are specified then node attributes are not considered. edge_match : callable A function that returns True if the edge attribute dictionaries for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should be considered equal during matching. The function will be called like edge_match(G1[u1][v1], G2[u2][v2]). That is, the function will receive the edge attribute dictionaries of the edges under consideration. Ignored if edge_subst_cost is specified. If neither edge_match nor edge_subst_cost are specified then edge attributes are not considered. node_subst_cost, node_del_cost, node_ins_cost : callable Functions that return the costs of node substitution, node deletion, and node insertion, respectively. The functions will be called like node_subst_cost(G1.nodes[n1], G2.nodes[n2]), node_del_cost(G1.nodes[n1]), node_ins_cost(G2.nodes[n2]). That is, the functions will receive the node attribute dictionaries as inputs. The functions are expected to return positive numeric values. Function node_subst_cost overrides node_match if specified. If neither node_match nor node_subst_cost are specified then default node substitution cost of 0 is used (node attributes are not considered during matching). If node_del_cost is not specified then default node deletion cost of 1 is used. If node_ins_cost is not specified then default node insertion cost of 1 is used. edge_subst_cost, edge_del_cost, edge_ins_cost : callable Functions that return the costs of edge substitution, edge deletion, and edge insertion, respectively. The functions will be called like edge_subst_cost(G1[u1][v1], G2[u2][v2]), edge_del_cost(G1[u1][v1]), edge_ins_cost(G2[u2][v2]). That is, the functions will receive the edge attribute dictionaries as inputs. The functions are expected to return positive numeric values. Function edge_subst_cost overrides edge_match if specified. If neither edge_match nor edge_subst_cost are specified then default edge substitution cost of 0 is used (edge attributes are not considered during matching). If edge_del_cost is not specified then default edge deletion cost of 1 is used. If edge_ins_cost is not specified then default edge insertion cost of 1 is used. upper_bound : numeric Maximum edit distance to consider. strictly_decreasing : bool If True, return consecutive approximations of strictly decreasing cost. Otherwise, return all edit paths of cost less than or equal to the previous minimum cost. Returns ------- Generator of tuples (node_edit_path, edge_edit_path, cost) node_edit_path : list of tuples (u, v) edge_edit_path : list of tuples ((u1, v1), (u2, v2)) cost : numeric See Also -------- graph_edit_distance, optimize_graph_edit_distance, optimal_edit_paths References ---------- .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick Martineau. An Exact Graph Edit Distance Algorithm for Solving Pattern Recognition Problems. 4th International Conference on Pattern Recognition Applications and Methods 2015, Jan 2015, Lisbon, Portugal. 2015, <10.5220/0005209202710278>. https://hal.archives-ouvertes.fr/hal-01168816 """ # TODO: support DiGraph import numpy as np from scipy.optimize import linear_sum_assignment class CostMatrix: def __init__(self, C, lsa_row_ind, lsa_col_ind, ls): #assert C.shape[0] == len(lsa_row_ind) #assert C.shape[1] == len(lsa_col_ind) #assert len(lsa_row_ind) == len(lsa_col_ind) #assert set(lsa_row_ind) == set(range(len(lsa_row_ind))) #assert set(lsa_col_ind) == set(range(len(lsa_col_ind))) #assert ls == C[lsa_row_ind, lsa_col_ind].sum() self.C = C self.lsa_row_ind = lsa_row_ind self.lsa_col_ind = lsa_col_ind self.ls = ls def make_CostMatrix(C, m, n): #assert(C.shape == (m + n, m + n)) lsa_row_ind, lsa_col_ind = linear_sum_assignment(C) # Fixup dummy assignments: # each substitution i<->j should have dummy assignment m+j<->n+i # NOTE: fast reduce of Cv relies on it #assert len(lsa_row_ind) == len(lsa_col_ind) indexes = zip(range(len(lsa_row_ind)), lsa_row_ind, lsa_col_ind) subst_ind = list(k for k, i, j in indexes if i < m and j < n) indexes = zip(range(len(lsa_row_ind)), lsa_row_ind, lsa_col_ind) dummy_ind = list(k for k, i, j in indexes if i >= m and j >= n) #assert len(subst_ind) == len(dummy_ind) lsa_row_ind[dummy_ind] = lsa_col_ind[subst_ind] + m lsa_col_ind[dummy_ind] = lsa_row_ind[subst_ind] + n return CostMatrix(C, lsa_row_ind, lsa_col_ind, C[lsa_row_ind, lsa_col_ind].sum()) def extract_C(C, i, j, m, n): #assert(C.shape == (m + n, m + n)) row_ind = [k in i or k - m in j for k in range(m + n)] col_ind = [k in j or k - n in i for k in range(m + n)] return C[row_ind, :][:, col_ind] def reduce_C(C, i, j, m, n): #assert(C.shape == (m + n, m + n)) row_ind = [k not in i and k - m not in j for k in range(m + n)] col_ind = [k not in j and k - n not in i for k in range(m + n)] return C[row_ind, :][:, col_ind] def reduce_ind(ind, i): #assert set(ind) == set(range(len(ind))) rind = ind[[k not in i for k in ind]] for k in set(i): rind[rind >= k] -= 1 return rind def match_edges(u, v, pending_g, pending_h, Ce, matched_uv=[]): """ Parameters: u, v: matched vertices, u=None or v=None for deletion/insertion pending_g, pending_h: lists of edges not yet mapped Ce: CostMatrix of pending edge mappings matched_uv: partial vertex edit path list of tuples (u, v) of previously matched vertex mappings u<->v, u=None or v=None for deletion/insertion Returns: list of (i, j): indices of edge mappings g<->h localCe: local CostMatrix of edge mappings (basically submatrix of Ce at cross of rows i, cols j) """ M = len(pending_g) N = len(pending_h) #assert Ce.C.shape == (M + N, M + N) g_ind = [i for i in range(M) if pending_g[i][:2] == (u, u) or any(pending_g[i][:2] in ((p, u), (u, p)) for p, q in matched_uv)] h_ind = [j for j in range(N) if pending_h[j][:2] == (v, v) or any(pending_h[j][:2] in ((q, v), (v, q)) for p, q in matched_uv)] m = len(g_ind) n = len(h_ind) if m or n: C = extract_C(Ce.C, g_ind, h_ind, M, N) #assert C.shape == (m + n, m + n) # Forbid structurally invalid matches # NOTE: inf remembered from Ce construction for k, i in zip(range(m), g_ind): g = pending_g[i][:2] for l, j in zip(range(n), h_ind): h = pending_h[j][:2] if nx.is_directed(G1) or nx.is_directed(G2): if any(g == (p, u) and h == (q, v) or g == (u, p) and h == (v, q) for p, q in matched_uv): continue else: if any(g in ((p, u), (u, p)) and h in ((q, v), (v, q)) for p, q in matched_uv): continue if g == (u, u): continue if h == (v, v): continue C[k, l] = inf localCe = make_CostMatrix(C, m, n) ij = list((g_ind[k] if k < m else M + h_ind[l], h_ind[l] if l < n else N + g_ind[k]) for k, l in zip(localCe.lsa_row_ind, localCe.lsa_col_ind) if k < m or l < n) else: ij = [] localCe = CostMatrix(np.empty((0, 0)), [], [], 0) return ij, localCe def reduce_Ce(Ce, ij, m, n): if len(ij): i, j = zip(*ij) m_i = m - sum(1 for t in i if t < m) n_j = n - sum(1 for t in j if t < n) return make_CostMatrix(reduce_C(Ce.C, i, j, m, n), m_i, n_j) else: return Ce def get_edit_ops(matched_uv, pending_u, pending_v, Cv, pending_g, pending_h, Ce, matched_cost): """ Parameters: matched_uv: partial vertex edit path list of tuples (u, v) of vertex mappings u<->v, u=None or v=None for deletion/insertion pending_u, pending_v: lists of vertices not yet mapped Cv: CostMatrix of pending vertex mappings pending_g, pending_h: lists of edges not yet mapped Ce: CostMatrix of pending edge mappings matched_cost: cost of partial edit path Returns: sequence of (i, j): indices of vertex mapping u<->v Cv_ij: reduced CostMatrix of pending vertex mappings (basically Cv with row i, col j removed) list of (x, y): indices of edge mappings g<->h Ce_xy: reduced CostMatrix of pending edge mappings (basically Ce with rows x, cols y removed) cost: total cost of edit operation NOTE: most promising ops first """ m = len(pending_u) n = len(pending_v) #assert Cv.C.shape == (m + n, m + n) # 1) a vertex mapping from optimal linear sum assignment i, j = min((k, l) for k, l in zip(Cv.lsa_row_ind, Cv.lsa_col_ind) if k < m or l < n) xy, localCe = match_edges(pending_u[i] if i < m else None, pending_v[j] if j < n else None, pending_g, pending_h, Ce, matched_uv) Ce_xy = reduce_Ce(Ce, xy, len(pending_g), len(pending_h)) #assert Ce.ls <= localCe.ls + Ce_xy.ls if prune(matched_cost + Cv.ls + localCe.ls + Ce_xy.ls): pass else: # get reduced Cv efficiently Cv_ij = CostMatrix(reduce_C(Cv.C, (i,), (j,), m, n), reduce_ind(Cv.lsa_row_ind, (i, m + j)), reduce_ind(Cv.lsa_col_ind, (j, n + i)), Cv.ls - Cv.C[i, j]) yield (i, j), Cv_ij, xy, Ce_xy, Cv.C[i, j] + localCe.ls # 2) other candidates, sorted by lower-bound cost estimate other = list() fixed_i, fixed_j = i, j if m <= n: candidates = ((t, fixed_j) for t in range(m + n) if t != fixed_i and (t < m or t == m + fixed_j)) else: candidates = ((fixed_i, t) for t in range(m + n) if t != fixed_j and (t < n or t == n + fixed_i)) for i, j in candidates: if prune(matched_cost + Cv.C[i, j] + Ce.ls): continue Cv_ij = make_CostMatrix(reduce_C(Cv.C, (i,), (j,), m, n), m - 1 if i < m else m, n - 1 if j < n else n) #assert Cv.ls <= Cv.C[i, j] + Cv_ij.ls if prune(matched_cost + Cv.C[i, j] + Cv_ij.ls + Ce.ls): continue xy, localCe = match_edges(pending_u[i] if i < m else None, pending_v[j] if j < n else None, pending_g, pending_h, Ce, matched_uv) if prune(matched_cost + Cv.C[i, j] + Cv_ij.ls + localCe.ls): continue Ce_xy = reduce_Ce(Ce, xy, len(pending_g), len(pending_h)) #assert Ce.ls <= localCe.ls + Ce_xy.ls if prune(matched_cost + Cv.C[i, j] + Cv_ij.ls + localCe.ls + Ce_xy.ls): continue other.append(((i, j), Cv_ij, xy, Ce_xy, Cv.C[i, j] + localCe.ls)) # yield from for t in sorted(other, key=lambda t: t[4] + t[1].ls + t[3].ls): yield t def get_edit_paths(matched_uv, pending_u, pending_v, Cv, matched_gh, pending_g, pending_h, Ce, matched_cost): """ Parameters: matched_uv: partial vertex edit path list of tuples (u, v) of vertex mappings u<->v, u=None or v=None for deletion/insertion pending_u, pending_v: lists of vertices not yet mapped Cv: CostMatrix of pending vertex mappings matched_gh: partial edge edit path list of tuples (g, h) of edge mappings g<->h, g=None or h=None for deletion/insertion pending_g, pending_h: lists of edges not yet mapped Ce: CostMatrix of pending edge mappings matched_cost: cost of partial edit path Returns: sequence of (vertex_path, edge_path, cost) vertex_path: complete vertex edit path list of tuples (u, v) of vertex mappings u<->v, u=None or v=None for deletion/insertion edge_path: complete edge edit path list of tuples (g, h) of edge mappings g<->h, g=None or h=None for deletion/insertion cost: total cost of edit path NOTE: path costs are non-increasing """ #debug_print('matched-uv:', matched_uv) #debug_print('matched-gh:', matched_gh) #debug_print('matched-cost:', matched_cost) #debug_print('pending-u:', pending_u) #debug_print('pending-v:', pending_v) #debug_print(Cv.C) #assert list(sorted(G1.nodes)) == list(sorted(list(u for u, v in matched_uv if u is not None) + pending_u)) #assert list(sorted(G2.nodes)) == list(sorted(list(v for u, v in matched_uv if v is not None) + pending_v)) #debug_print('pending-g:', pending_g) #debug_print('pending-h:', pending_h) #debug_print(Ce.C) #assert list(sorted(G1.edges)) == list(sorted(list(g for g, h in matched_gh if g is not None) + pending_g)) #assert list(sorted(G2.edges)) == list(sorted(list(h for g, h in matched_gh if h is not None) + pending_h)) #debug_print() if prune(matched_cost + Cv.ls + Ce.ls): return if not max(len(pending_u), len(pending_v)): #assert not len(pending_g) #assert not len(pending_h) # path completed! #assert matched_cost <= maxcost.value maxcost.value = min(maxcost.value, matched_cost) yield matched_uv, matched_gh, matched_cost else: edit_ops = get_edit_ops(matched_uv, pending_u, pending_v, Cv, pending_g, pending_h, Ce, matched_cost) for ij, Cv_ij, xy, Ce_xy, edit_cost in edit_ops: i, j = ij #assert Cv.C[i, j] + sum(Ce.C[t] for t in xy) == edit_cost if prune(matched_cost + edit_cost + Cv_ij.ls + Ce_xy.ls): continue # dive deeper u = pending_u.pop(i) if i < len(pending_u) else None v = pending_v.pop(j) if j < len(pending_v) else None matched_uv.append((u, v)) for x, y in xy: len_g = len(pending_g) len_h = len(pending_h) matched_gh.append((pending_g[x] if x < len_g else None, pending_h[y] if y < len_h else None)) sortedx = list(sorted(x for x, y in xy)) sortedy = list(sorted(y for x, y in xy)) G = list((pending_g.pop(x) if x < len(pending_g) else None) for x in reversed(sortedx)) H = list((pending_h.pop(y) if y < len(pending_h) else None) for y in reversed(sortedy)) # yield from for t in get_edit_paths(matched_uv, pending_u, pending_v, Cv_ij, matched_gh, pending_g, pending_h, Ce_xy, matched_cost + edit_cost): yield t # backtrack if u is not None: pending_u.insert(i, u) if v is not None: pending_v.insert(j, v) matched_uv.pop() for x, g in zip(sortedx, reversed(G)): if g is not None: pending_g.insert(x, g) for y, h in zip(sortedy, reversed(H)): if h is not None: pending_h.insert(y, h) for t in xy: matched_gh.pop() # Initialization pending_u = list(G1.nodes) pending_v = list(G2.nodes) # cost matrix of vertex mappings m = len(pending_u) n = len(pending_v) C = np.zeros((m + n, m + n)) if node_subst_cost: C[0:m, 0:n] = np.array([node_subst_cost(G1.nodes[u], G2.nodes[v]) for u in pending_u for v in pending_v] ).reshape(m, n) elif node_match: C[0:m, 0:n] = np.array([1 - int(node_match(G1.nodes[u], G2.nodes[v])) for u in pending_u for v in pending_v] ).reshape(m, n) else: # all zeroes pass #assert not min(m, n) or C[0:m, 0:n].min() >= 0 if node_del_cost: del_costs = [node_del_cost(G1.nodes[u]) for u in pending_u] else: del_costs = [1] * len(pending_u) #assert not m or min(del_costs) >= 0 if node_ins_cost: ins_costs = [node_ins_cost(G2.nodes[v]) for v in pending_v] else: ins_costs = [1] * len(pending_v) #assert not n or min(ins_costs) >= 0 inf = C[0:m, 0:n].sum() + sum(del_costs) + sum(ins_costs) + 1 C[0:m, n:n + m] = np.array([del_costs[i] if i == j else inf for i in range(m) for j in range(m)] ).reshape(m, m) C[m:m + n, 0:n] = np.array([ins_costs[i] if i == j else inf for i in range(n) for j in range(n)] ).reshape(n, n) Cv = make_CostMatrix(C, m, n) #debug_print('Cv: {} x {}'.format(m, n)) #debug_print(Cv.C) pending_g = list(G1.edges) pending_h = list(G2.edges) # cost matrix of edge mappings m = len(pending_g) n = len(pending_h) C = np.zeros((m + n, m + n)) if edge_subst_cost: C[0:m, 0:n] = np.array([edge_subst_cost(G1.edges[g], G2.edges[h]) for g in pending_g for h in pending_h] ).reshape(m, n) elif edge_match: C[0:m, 0:n] = np.array([1 - int(edge_match(G1.edges[g], G2.edges[h])) for g in pending_g for h in pending_h] ).reshape(m, n) else: # all zeroes pass #assert not min(m, n) or C[0:m, 0:n].min() >= 0 if edge_del_cost: del_costs = [edge_del_cost(G1.edges[g]) for g in pending_g] else: del_costs = [1] * len(pending_g) #assert not m or min(del_costs) >= 0 if edge_ins_cost: ins_costs = [edge_ins_cost(G2.edges[h]) for h in pending_h] else: ins_costs = [1] * len(pending_h) #assert not n or min(ins_costs) >= 0 inf = C[0:m, 0:n].sum() + sum(del_costs) + sum(ins_costs) + 1 C[0:m, n:n + m] = np.array([del_costs[i] if i == j else inf for i in range(m) for j in range(m)] ).reshape(m, m) C[m:m + n, 0:n] = np.array([ins_costs[i] if i == j else inf for i in range(n) for j in range(n)] ).reshape(n, n) Ce = make_CostMatrix(C, m, n) #debug_print('Ce: {} x {}'.format(m, n)) #debug_print(Ce.C) #debug_print() class MaxCost: def __init__(self): # initial upper-bound estimate # NOTE: should work for empty graph self.value = Cv.C.sum() + Ce.C.sum() + 1 maxcost = MaxCost() def prune(cost): if upper_bound is not None: if cost > upper_bound: return True if cost > maxcost.value: return True elif strictly_decreasing and cost >= maxcost.value: return True # Now go! for vertex_path, edge_path, cost in \ get_edit_paths([], pending_u, pending_v, Cv, [], pending_g, pending_h, Ce, 0): #assert sorted(G1.nodes) == sorted(u for u, v in vertex_path if u is not None) #assert sorted(G2.nodes) == sorted(v for u, v in vertex_path if v is not None) #assert sorted(G1.edges) == sorted(g for g, h in edge_path if g is not None) #assert sorted(G2.edges) == sorted(h for g, h in edge_path if h is not None) #print(vertex_path, edge_path, cost, file = sys.stderr) #assert cost == maxcost.value yield list(vertex_path), list(edge_path), cost def setup_module(module): """Fixture for nose tests.""" from nose import SkipTest try: import numpy except: raise SkipTest("NumPy not available") try: import scipy except: raise SkipTest("SciPy not available")