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Improve method _ford fulkerson chronicle in src/sage/combinat/posets/posets.py #37571

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Mar 31, 2024
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Improve method _ford fulkerson chronicle in src/sage/combinat/posets/posets.py #37571

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4895293
improve _ford_fulkerson_chronicles and a few details
dcoudert Mar 9, 2024
58b8506
further details
dcoudert Mar 9, 2024
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131 changes: 73 additions & 58 deletions src/sage/combinat/posets/posets.py
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Original file line number Diff line number Diff line change
Expand Up @@ -718,8 +718,8 @@
if len(data) == 2: # types 1 or 2
if callable(data[1]): # type 2
elements, function = data
relations = [[x, y] for x in elements for y in elements
if function(x, y)]
relations = ((x, y) for x in elements for y in elements
if function(x, y))
else: # type 1
elements, relations = data
# check that relations are relations
Expand Down Expand Up @@ -1079,10 +1079,10 @@
for i in elements)
# Relabel using the linear_extension.
# So range(len(D)) becomes a linear extension of the poset.
rdict = {self._elements[i]: i for i in range(len(self._elements))}
self._hasse_diagram = HasseDiagram(hasse_diagram.relabel(rdict, inplace=False), data_structure="static_sparse")
self._element_to_vertex_dict = {self._elements[i]: i
for i in range(len(self._elements))}
rdict = {element: i for i, element in enumerate(self._elements)}
self._hasse_diagram = HasseDiagram(hasse_diagram.relabel(rdict, inplace=False),
data_structure="static_sparse")
self._element_to_vertex_dict = rdict
self._is_facade = facade

@lazy_attribute
Expand Down Expand Up @@ -1110,8 +1110,8 @@
if self._is_facade:
return self._elements
else:
return tuple(self.element_class(self, self._elements[vertex], vertex)
for vertex in range(len(self._elements)))
return tuple(self.element_class(self, element, vertex)
for vertex, element in enumerate(self._elements))

# This defines the type (class) of elements of poset.
Element = PosetElement
Expand Down Expand Up @@ -2366,8 +2366,7 @@
mt = self._hasse_diagram._meet
if mt[i, j] == -1:
return None
else:
return self._vertex_to_element(mt[i, j])
return self._vertex_to_element(mt[i, j])

def join(self, x, y):
r"""
Expand Down Expand Up @@ -2400,8 +2399,7 @@
jn = self._hasse_diagram._join
if jn[i, j] == -1:
return None
else:
return self._vertex_to_element(jn[i, j])
return self._vertex_to_element(jn[i, j])

def is_d_complete(self) -> bool:
r"""
Expand Down Expand Up @@ -2992,12 +2990,11 @@
i, j = map(self._element_to_vertex, (x, y))
if i == j:
return 0
elif self._hasse_diagram.is_less_than(i, j):
if self._hasse_diagram.is_less_than(i, j):
return -1
elif self._hasse_diagram.is_less_than(j, i):
if self._hasse_diagram.is_less_than(j, i):
return 1
else:
return None
return None

def minimal_elements(self):
"""
Expand Down Expand Up @@ -3049,8 +3046,7 @@
hasse_bot = self._hasse_diagram.bottom()
if hasse_bot is None:
return None
else:
return self._vertex_to_element(hasse_bot)
return self._vertex_to_element(hasse_bot)

def has_bottom(self):
"""
Expand Down Expand Up @@ -3105,8 +3101,7 @@
hasse_top = self._hasse_diagram.top()
if hasse_top is None:
return None
else:
return self._vertex_to_element(hasse_top)
return self._vertex_to_element(hasse_top)

def has_top(self):
"""
Expand Down Expand Up @@ -3185,7 +3180,7 @@
max_chain.reverse()
return (height, max_chain)

def has_isomorphic_subposet(self, other):
def has_isomorphic_subposet(self, other) -> bool:
"""
Return ``True`` if the poset contains a subposet isomorphic to
``other``.
Expand All @@ -3210,13 +3205,10 @@

sage: len([P for P in Posets(5) if P.has_isomorphic_subposet(D)])
11

"""
if not hasattr(other, 'hasse_diagram'):
raise TypeError("'other' is not a finite poset")
if self._hasse_diagram.transitive_closure().subgraph_search(other._hasse_diagram.transitive_closure(), induced=True) is None:
return False
return True
return self._hasse_diagram.transitive_closure().subgraph_search(other._hasse_diagram.transitive_closure(), induced=True) is not None

def is_bounded(self) -> bool:
"""
Expand Down Expand Up @@ -3331,12 +3323,12 @@
if ordered:
sorted_o = elms
return all(self.lt(a, b) for a, b in zip(sorted_o, sorted_o[1:]))
else:
# _element_to_vertex can be assumed to be a linear extension
# of the poset according to the documentation of class
# HasseDiagram.
sorted_o = sorted(elms, key=self._element_to_vertex)
return all(self.le(a, b) for a, b in zip(sorted_o, sorted_o[1:]))

# _element_to_vertex can be assumed to be a linear extension
# of the poset according to the documentation of class
# HasseDiagram.
sorted_o = sorted(elms, key=self._element_to_vertex)
return all(self.le(a, b) for a, b in zip(sorted_o, sorted_o[1:]))

def is_antichain_of_poset(self, elms):
"""
Expand Down Expand Up @@ -3494,14 +3486,14 @@
max_chains = sorted([[label_dict[(chain[i], chain[i + 1])]
for i in range(len(chain) - 1)]
for chain in P.maximal_chains_iterator()])
if max_chains[0] != sorted(max_chains[0]) or any(max_chains[i] == sorted(max_chains[i]) for i in range(1, len(max_chains))):
if (max_chains[0] != sorted(max_chains[0]) or
any(max_chains[i] == sorted(max_chains[i]) for i in range(1, len(max_chains)))):
return False
elif return_raising_chains:
if return_raising_chains:
raising_chains[(a, b)] = max_chains[0]
if return_raising_chains:
return raising_chains
else:
return True
return True

def dimension(self, certificate=False, *, solver=None, integrality_tolerance=1e-3):
r"""
Expand Down Expand Up @@ -3650,7 +3642,7 @@
"""
p = MixedIntegerLinearProgram(constraint_generation=True, solver=solver)
b = p.new_variable(binary=True)
for (u, v) in inc_P: # Each point has a color
for u, v in inc_P: # Each point has a color
p.add_constraint(p.sum(b[(u, v), i] for i in range(k)) == 1)
p.add_constraint(p.sum(b[(v, u), i] for i in range(k)) == 1)
for cycle in cycles: # No monochromatic set
Expand Down Expand Up @@ -4632,8 +4624,7 @@
if hasattr(other, 'hasse_diagram'):
return self.hasse_diagram().is_isomorphic(other.hasse_diagram(),
**kwds)
else:
raise TypeError("'other' is not a finite poset")
raise TypeError("'other' is not a finite poset")

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def isomorphic_subposets_iterator(self, other):
"""
Expand Down Expand Up @@ -8310,7 +8301,15 @@
sage: ps = [[16,12,14,-13],[[12,14],[14,-13],[12,16],[16,-13]]]
sage: G, e = Poset(ps).frank_network()
sage: G.edges(sort=True)
[((-1, 0), (0, -13), None), ((-1, 0), (0, 12), None), ((-1, 0), (0, 14), None), ((-1, 0), (0, 16), None), ((0, -13), (1, -13), None), ((0, -13), (1, 12), None), ((0, -13), (1, 14), None), ((0, -13), (1, 16), None), ((0, 12), (1, 12), None), ((0, 14), (1, 12), None), ((0, 14), (1, 14), None), ((0, 16), (1, 12), None), ((0, 16), (1, 16), None), ((1, -13), (2, 0), None), ((1, 12), (2, 0), None), ((1, 14), (2, 0), None), ((1, 16), (2, 0), None)]
[((-1, 0), (0, -13), None), ((-1, 0), (0, 12), None),
((-1, 0), (0, 14), None), ((-1, 0), (0, 16), None),
((0, -13), (1, -13), None), ((0, -13), (1, 12), None),
((0, -13), (1, 14), None), ((0, -13), (1, 16), None),
((0, 12), (1, 12), None), ((0, 14), (1, 12), None),
((0, 14), (1, 14), None), ((0, 16), (1, 12), None),
((0, 16), (1, 16), None), ((1, -13), (2, 0), None),
((1, 12), (2, 0), None), ((1, 14), (2, 0), None),
((1, 16), (2, 0), None)]
sage: e
{((-1, 0), (0, -13)): 0,
((-1, 0), (0, 12)): 0,
Expand Down Expand Up @@ -9078,14 +9077,16 @@
EXAMPLES::

sage: from sage.combinat.posets.posets import _ford_fulkerson_chronicle
sage: G = DiGraph({1: [3,6,7], 2: [4], 3: [7], 4: [], 6: [7,8], 7: [9], 8: [9,12], 9: [], 10: [], 12: []})
sage: G = DiGraph({1: [3, 6, 7], 2: [4], 3: [7], 4: [], 6: [7, 8],
....: 7: [9], 8: [9, 12], 9: [], 10: [], 12: []})
sage: s = 1
sage: t = 9
sage: (1, 6, None) in G.edges(sort=False)
True
sage: (1, 6) in G.edges(sort=False)
False
sage: a = {(1, 6): 4, (2, 4): 0, (1, 3): 4, (1, 7): 1, (3, 7): 6, (7, 9): 1, (6, 7): 3, (6, 8): 1, (8, 9): 0, (8, 12): 2}
sage: a = {(1, 6): 4, (2, 4): 0, (1, 3): 4, (1, 7): 1, (3, 7): 6,
....: (7, 9): 1, (6, 7): 3, (6, 8): 1, (8, 9): 0, (8, 12): 2}
sage: ffc = _ford_fulkerson_chronicle(G, s, t, a)
sage: next(ffc)
(1, 0)
Expand Down Expand Up @@ -9114,33 +9115,47 @@
sage: next(ffc)
(11, 2)
"""
# pi: potential function as a dictionary.
pi = {v: 0 for v in G}
n = G.order()
m = G.size()

# Make a copy of the graph with vertices relabeled 0..n-1
index_to_vertex = list(G)
vertex_to_index = {u: i for i, u in enumerate(index_to_vertex)}
G = G.relabel(perm=vertex_to_index, inplace=False)
s = vertex_to_index[s]
t = vertex_to_index[t]
# Associate each edge to an integer, its index
index_to_edge = list(G.edge_iterator(labels=False))
edge_to_index = {e: i for i, e in enumerate(index_to_edge)}
# Change the cost function to a vector indexed by edge indices
a = [a[index_to_vertex[u], index_to_vertex[v]] for u, v in index_to_edge]

# pi: potential function as a vector indexed by vertices.
pi = [0 for _ in range(n)]
# p: value of the potential pi.
p = 0

# f: flow function as a dictionary.
f = {edge: 0 for edge in G.edge_iterator(labels=False)}
# f: flow function as a vector indexed by edge indices
f = [0 for _ in range(m)]
# val: value of the flow f. (Cannot call it v due to Python's asinine
# handling of for loops.)
val = 0

# capacity: capacity function as a dictionary. Here, just the
# indicator function of the set of arcs of G.
capacity = {edge: 1 for edge in G.edge_iterator(labels=False)}
# capacity: capacity function as a vector indexed by edge indices. Here,
# just the indicator function of the set of arcs of G.
capacity = [1 for _ in range(m)]

while True:

# Step MC1 in Britz-Fomin, Algorithm 7.2.

# Gprime: directed graph G' from Britz-Fomin, Section 7.
Gprime = DiGraph()
Gprime.add_vertices(G)
for u, v in G.edge_iterator(labels=False):
if pi[v] - pi[u] == a[(u, v)]:
if f[(u, v)] < capacity[(u, v)]:
Gprime = DiGraph(n)
for e_index, (u, v) in enumerate(index_to_edge):
if pi[v] - pi[u] == a[e_index]:
if f[e_index] < capacity[e_index]:
Gprime.add_edge(u, v)
elif f[(u, v)] > 0:
elif f[e_index] > 0:
Gprime.add_edge(v, u)

# X: list of vertices of G' reachable from s
Expand All @@ -9150,14 +9165,14 @@
shortest_path = Gprime.shortest_path(s, t, by_weight=False)
shortest_path_in_edges = zip(shortest_path[:-1], shortest_path[1:])
for u, v in shortest_path_in_edges:
if v in G.neighbor_out_iterator(u):
f[(u, v)] += 1
if (u, v) in edge_to_index:
f[edge_to_index[u, v]] += 1
else:
f[(v, u)] -= 1
f[edge_to_index[v, u]] -= 1
val += 1
else:
# Step MC2b in Britz-Fomin, Algorithm 7.2.
for v in G:
for v in range(n):
if v not in X:
pi[v] += 1
p += 1
Expand Down
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