def get_node_by_treewidth_reduction(graph):
"""
Returns a list of pairs (node : reduction_in_treewidth) for the
provided graph. The graph is **ASSUMED** to be in the optimal
elimination order, e.g. the nodes have to be relabelled by
peo
Parameters
----------
graph : networkx.Graph without self-loops and parallel edges
Returns
-------
nodes_by_treewidth_reduction : dict
"""
# Get flop cost of the bucket elimination
initial_treewidth = get_treewidth_from_peo(
graph, sorted(graph.nodes))
nodes_by_treewidth_reduction = []
for node in graph.nodes(data=False):
reduced_graph = copy.deepcopy(graph)
# Take out one node
remove_node(reduced_graph, node)
treewidth = get_treewidth_from_peo(
reduced_graph, sorted(reduced_graph.nodes))
delta = initial_treewidth - treewidth
nodes_by_treewidth_reduction.append((node, delta))
return nodes_by_treewidth_reduction
def test_maximum_cardinality_search():
"""Test maximum cardinality search algorithm"""
# Read graph
import qtree.operators as ops
import os
this_dir = os.path.dirname((os.path.abspath(__file__)))
nq, c = ops.read_circuit_file(this_dir + '/../../inst_2x2_7_0.txt')
old_g, *_ = circ2graph(nq, c)
# Make random clique
vertices = list(np.random.choice(old_g.nodes, 4, replace=False))
while is_clique(old_g, vertices):
vertices = list(np.random.choice(old_g.nodes, 4, replace=False))
g = make_clique_on(old_g, vertices)
# Make graph completion
peo, tw = get_peo(g)
g_chordal = get_fillin_graph2(g, peo)
# MCS will produce alternative PEO with this clique at the end
new_peo = maximum_cardinality_search(g_chordal, list(vertices))
# Test if new peo is correct
assert is_peo_zero_fillin(g_chordal, peo)
assert is_peo_zero_fillin(g_chordal, new_peo)
new_tw = get_treewidth_from_peo(g, new_peo)
assert tw == new_tw
print('peo:', peo)
print('new_peo:', new_peo)
def test_tree_to_peo():
"""
Test tree reduction algorithm and also
the conversion of tree to peo
"""
g, peo = make_test_graph()
f = get_tree_from_peo(g, peo)
fd, el = get_reduced_tree(f, 1)
peo = get_peo_from_tree(fd, [5, 6])
g.remove_nodes_from(el)
tw1 = get_treewidth_from_peo(g, peo)
tw2 = len(find_max_cliques(fd)[0]) - 1
assert tw1 == tw2
def test_tree_reduction():
"""
Tests the deletion of variables from tree
"""
g, peo = make_test_graph()
f = get_tree_from_peo(g, peo)
ff = rm_element_in_tree(f, 2)
peo.remove(2)
g.remove_node(2)
tw1 = get_treewidth_from_peo(g, peo)
tw2 = len(find_max_cliques(ff)[0]) - 1
assert tw1 == tw2