def make_dag(g: DirectedGraph,
s: int,
t: int,
pmap_vpreds: ReadPropertyMap,
single_path: bool = False) -> set:
"""
Extracts the arcs related to shortest paths from `s`
to `t` in a graph `g` given the predecessors map computed
using `dijkstra_shortest_paths` from `s`.
Args:
g: The graph.
s: The target's vertex descriptor.
t: The target's vertex descriptor.
pmap_vpreds: The `ReadPropertyMap{int : set(int)}` mapping each
vertex with its set of (direct) predecessors.
single_path: Pass True to extract a single path. If multiple
paths exist from `s` to `t`, this extracts an arbitrary
path instead of all of them.
Returns:
The corresponding set of `EdgeDescriptor`s.
"""
kept_edges = set()
n_prev = -1
n = 0
to_process = {t}
done = set()
while to_process:
es = {e for u in to_process if pmap_vpreds[u] for e in pmap_vpreds[u]}
if single_path and es:
es = {es.pop()}
kept_edges |= es
predecessors = {source(e, g) for e in es if e not in done}
done |= to_process
to_process = predecessors - done
return kept_edges
def examine_relevant_edge(self, e: EdgeDescriptor, g: Graph):
u = source(e, g)
v = target(e, g)
u_dup = self.m_pmap_vertices[u]
v_dup = self.m_pmap_vertices[
v] if v in self.m_dup_vertices else self.dup_vertex(v, g)
(e_dup, _) = add_edge(u_dup, v_dup, self.m_g_dup)
if self.m_pmap_edges:
self.m_pmap_edges[e] = e_dup
if self.m_callback_dup_edge:
self.m_callback_dup_edge(e, g, e_dup, self.m_g_dup)
def make_gdp2() -> GraphDp:
g = make_g()
vlabel = {u : "v%s" % u for u in vertices(g)}
elabel = {e : "e%s%s" % (source(e, g), target(e, g)) for e in edges(g)}
gdp = GraphDp(
g,
dpv = {
"label" : make_assoc_property_map(vlabel),
"color" : make_func_property_map(lambda q: "red" if q % 2 else "green"),
},
dpe = {
"label" : make_assoc_property_map(elabel),
"color" : make_func_property_map(lambda e: "red" if target(e, g) % 2 else "green"),
}
)
return gdp
def edge_color(e, g, pmap_component, pmap_color, default_color = "black"):
"""
Returns the color assigned to an edge.
Args:
e: An EdgeDescriptor.
g: A DirectedGraph.
pmap_component: A ReadPropertyMap, mapping a vertex with its strongly
connected component.
pmap_color: A ReadPropertyMap, mapping a component ID with a color.
default_color: color returned if the color of the source and the
target of e mismatch.
"""
u = source(e, g)
v = target(e, g)
color_u = pmap_color[pmap_component[u]]
color_v = pmap_color[pmap_component[v]]
return color_u if color_u == color_v else default_color
def cut(s: int, g: Graph, in_cut) -> set:
"""
Find a vertex cut given an edge cut.
Args:
g: A `Graph` instance corresponding to an acyclic graph.
s: The `VertexDescriptor` corresponding to the source vertex.
in_cut: `Callback(EdgeDescriptor, Graph) -> bool` indicating whether an
edge belong to the considered cut.
"""
class LeavesVisitor(DefaultDepthFirstSearchVisitor):
def __init__(self, leaves: set):
self.leaves = leaves
def examine_edge(self, e: EdgeDescriptor, g: Graph):
u = source(e, g)
self.leaves.discard(u)
def discover_vertex(self, u: int, g: Graph):
self.leaves.add(u)
class IfPush:
def __init__(self, in_cut, cutting_edges: set):
self.in_cut = in_cut
self.cutting_edges = cutting_edges
def __call__(self, e: EdgeDescriptor, g: Graph) -> bool:
is_cutting_edge = self.in_cut(e, g)
if is_cutting_edge:
self.cutting_edges.add(e)
return not is_cutting_edge
leaves = set()
cutting_edges = set()
map_vcolor = defaultdict(int)
depth_first_search(s,
g,
pmap_vcolor=make_assoc_property_map(map_vcolor),
vis=LeavesVisitor(leaves),
if_push=IfPush(in_cut, cutting_edges))
return {target(e, g)
for e in cutting_edges
} | {u
for u in leaves} - {source(e, g)
for e in cutting_edges}
def test_directed_graph(links: list = LINKS):
map_eweight = dict()
pmap_eweight = make_assoc_property_map(map_eweight)
g = make_graph(LINKS,
pmap_eweight,
directed=True,
build_reverse_edge=False)
map_vpreds = defaultdict(set)
map_vdist = dict()
dijkstra_shortest_paths(g, 0, pmap_eweight,
make_assoc_property_map(map_vpreds),
make_assoc_property_map(map_vdist))
infty = sys.maxsize
E = {(source(e, g), target(e, g)): e for e in edges(g)}
assert map_vpreds == {
1: {E[0, 1]},
2: {E[1, 2]},
3: {E[1, 3]},
4: {E[3, 4]},
5: {E[4, 5]},
6: {E[4, 6]},
7: {E[6, 7]},
8: {E[7, 8]},
9: {E[7, 9]}
}
assert map_vdist == {
0: 0,
1: 1,
2: 2,
3: 4,
4: 5,
5: 6,
6: 6,
7: 14,
8: 15,
9: 15,
10: infty
}
def make_path(g: DirectedGraph, s: int, t: int,
pmap_vpreds: ReadPropertyMap) -> list:
"""
Extract the path from `s` to `t` in a graph `g` gien
to `t` in a graph `g` given the predecessors map computed
using `dijkstra_shortest_paths` from `s`.
Args:
g: The graph.
s: The target's vertex descriptor.
t: The target's vertex descriptor.
pmap_vpreds: A `ReadPropertyMap{int : set(int)}` mapping each
vertex with its set of (direct) predecessors.
Returns:
A list of consecutive arcs forming a shortest path from `s` of `t`.
If several shortest paths exist from `s` to `t`, this function returns
an arbitrary path.
"""
arcs = make_dag(g, s, t, pmap_vpreds, single_path=True)
path = list(arcs)
path.sort(key=lambda e: (source(e, g), target(e, g)))
return path
def edge_to_pair(e: EdgeDescriptor, g: DirectedGraph) -> tuple:
return (source(e, g), target(e, g))
def test_graph_copy_small(threshold :int = 50):
g = DirectedGraph(5)
(e01, _) = add_edge(0, 1, g)
(e02, _) = add_edge(0, 2, g)
(e04, _) = add_edge(0, 4, g)
(e12, _) = add_edge(1, 2, g)
(e23, _) = add_edge(2, 3, g)
(e24, _) = add_edge(2, 4, g)
(e40, _) = add_edge(4, 0, g)
(e44, _) = add_edge(4, 4, g)
map_eweight = {
e01 : 83,
e02 : 3,
e04 : 78,
e12 : 92,
e23 : 7,
e24 : 18,
e40 : 51,
e44 : 84,
}
pmap_eweight = make_assoc_property_map(map_eweight)
pmap_erelevant = make_func_property_map(lambda e: pmap_eweight[e] >= threshold)
g_dup = DirectedGraph(0)
# Edge duplicate
map_eweight_dup = dict()
pmap_eweight_dup = make_assoc_property_map(map_eweight_dup)
def callback_dup_edge(e, g, e_dup, g_dup):
pmap_eweight_dup[e_dup] = pmap_eweight[e]
# Vertex mapping
map_vertices = dict()
pmap_vertices = make_assoc_property_map(map_vertices)
map_edges = dict()
pmap_edges = make_assoc_property_map(map_edges)
graph_copy(
0, g, g_dup,
pmap_erelevant = pmap_erelevant,
pmap_vertices = pmap_vertices,
pmap_edges = pmap_edges,
callback_dup_edge = callback_dup_edge
)
if in_ipynb():
ori_html = dotstr_to_html(
GraphDp(
g,
dpv = {
"label" : make_func_property_map(lambda u: "%s<br/>(becomes %s)" % (u, pmap_vertices[u]))
},
dpe = {
"color" : make_func_property_map(lambda e : "darkgreen" if pmap_erelevant[e] else "lightgrey"),
"style" : make_func_property_map(lambda e : "solid" if pmap_erelevant[e] else "dashed"),
"label" : pmap_eweight,
}
).to_dot()
)
dup_html = dotstr_to_html(
GraphDp(
g_dup,
dpe = {
"label" : pmap_eweight_dup,
}
).to_dot()
)
html(
"""
<table>
<tr>
<th>Original</th>
<th>Extracted</th>
</tr><tr>
<td>%s</td>
<td>%s</td>
</tr>
</table>
""" % (ori_html, dup_html)
)
if threshold == 50:
expected_num_edges = 5
assert map_vertices == {
0 : 0,
1 : 1,
2 : 2,
4 : 3
}
for e, e_dup in map_edges.items():
u = source(e, g)
v = target(e, g)
u_dup = source(e_dup, g_dup)
v_dup = target(e_dup, g_dup)
assert u_dup == pmap_vertices[u], "u_dup = %s ; pmap_vertices[%s] = %s" % (u_dup, u, pmap_vertices[u])
assert v_dup == pmap_vertices[v], "v_dup = %s ; pmap_vertices[%s] = %s" % (v_dup, v, pmap_vertices[v])
assert pmap_eweight[e] == pmap_eweight_dup[e_dup]
elif threshold < min([w for w in map_eweight.values()]):
expected_num_edges = num_edges(g)
elif threshold > max([w for w in map_eweight.values()]):
expected_num_edges = 0
assert expected_num_edges == num_edges(g_dup), \
"""
Invalid edge number:
Expected: %s
Obtained: %s
""" % (expected_num_edges, num_edges(g_dup))
def examine_edge(self, e: EdgeDescriptor, g: Graph):
u = source(e, g)
self.leaves.discard(u)
