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improve graph traversal methods #39217

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merged 5 commits into from
Jan 4, 2025
Merged

improve graph traversal methods #39217

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56edd95
avoid conversion in lex_M_fast
dcoudert Dec 28, 2024
02fee8f
avoid conversion in maximum_cardinality_search
dcoudert Dec 28, 2024
97b0d9b
add doctest to maximum_cardinality_search
dcoudert Dec 28, 2024
d05de5b
use pairing heap in maximum_cardinality_search
dcoudert Dec 28, 2024
438865c
avoid conversion in maximum_cardinality_search_M
dcoudert Dec 28, 2024
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159 changes: 113 additions & 46 deletions src/sage/graphs/traversals.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -63,16 +63,17 @@ from collections import deque

from libc.string cimport memset
from libc.stdint cimport uint32_t
from libcpp.queue cimport priority_queue
from libcpp.pair cimport pair
from libcpp.vector cimport vector
from cysignals.signals cimport sig_on, sig_off
from memory_allocator cimport MemoryAllocator

from sage.data_structures.pairing_heap cimport PairingHeap_of_n_integers
from sage.graphs.base.c_graph cimport CGraph, CGraphBackend
from sage.graphs.base.static_sparse_backend cimport StaticSparseCGraph
from sage.graphs.base.static_sparse_backend cimport StaticSparseBackend
from sage.graphs.base.static_sparse_graph cimport init_short_digraph
from sage.graphs.base.static_sparse_graph cimport free_short_digraph
from sage.graphs.base.static_sparse_graph cimport out_degree
from sage.graphs.base.c_graph cimport CGraph, CGraphBackend
from sage.graphs.graph_decompositions.slice_decomposition cimport \
extended_lex_BFS

Expand Down Expand Up @@ -753,8 +754,7 @@ def lex_M(self, triangulation=False, labels=False, initial_vertex=None, algorith
- ``labels`` -- boolean (default: ``False``); whether to return the labels
assigned to each vertex

- ``initial_vertex`` -- (default: ``None``) the first vertex to
consider
- ``initial_vertex`` -- (default: ``None``); the first vertex to consider

- ``algorithm`` -- string (default: ``None``); one of the following
algorithms:
Expand Down Expand Up @@ -820,6 +820,18 @@ def lex_M(self, triangulation=False, labels=False, initial_vertex=None, algorith
sage: g.lex_M()
[6, 4, 5, 3, 2, 1]

The ordering depends on the initial vertex::

sage: G = graphs.HouseGraph()
sage: G.lex_M(algorithm='lex_M_slow', initial_vertex=0)
[4, 3, 2, 1, 0]
sage: G.lex_M(algorithm='lex_M_slow', initial_vertex=2)
[1, 4, 3, 0, 2]
sage: G.lex_M(algorithm='lex_M_fast', initial_vertex=0)
[4, 3, 2, 1, 0]
sage: G.lex_M(algorithm='lex_M_fast', initial_vertex=2)
[1, 4, 3, 0, 2]

TESTS:

``'lex_M_fast'`` cannot return labels::
Expand Down Expand Up @@ -1127,6 +1139,18 @@ def lex_M_fast(G, triangulation=False, initial_vertex=None):
Traceback (most recent call last):
...
ValueError: 'foo' is not a graph vertex

Immutable graphs::

sage: from sage.graphs.traversals import lex_M_fast
sage: G = graphs.RandomGNP(10, .7)
sage: G._backend
<sage.graphs.base.sparse_graph.SparseGraphBackend ...>
sage: H = Graph(G, immutable=True)
sage: H._backend
<sage.graphs.base.static_sparse_backend.StaticSparseBackend ...>
sage: lex_M_fast(G) == lex_M_fast(H)
True
"""
if initial_vertex is not None and initial_vertex not in G:
raise ValueError("'{}' is not a graph vertex".format(initial_vertex))
Expand All @@ -1136,23 +1160,31 @@ def lex_M_fast(G, triangulation=False, initial_vertex=None):

# ==> Initialization

cdef list int_to_v = list(G)
cdef int i, j, k, v, w, z

if initial_vertex is not None:
# We put the initial vertex at first place in the ordering
i = int_to_v.index(initial_vertex)
int_to_v[0], int_to_v[i] = int_to_v[i], int_to_v[0]

cdef list int_to_v
cdef StaticSparseCGraph cg
cdef short_digraph sd
init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_v)
if isinstance(G, StaticSparseBackend):
cg = <StaticSparseCGraph> G._cg
sd = <short_digraph> cg.g
int_to_v = cg._vertex_to_labels
else:
int_to_v = list(G)
init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_v)

cdef uint32_t* p_tmp
cdef uint32_t* p_end

cdef int n = G.order()

cdef list unnumbered_vertices = list(range(n))

if initial_vertex is not None:
# We put the initial vertex at the first place
i = int_to_v.index(initial_vertex)
unnumbered_vertices[0], unnumbered_vertices[i] = unnumbered_vertices[i], unnumbered_vertices[0]

cdef MemoryAllocator mem = MemoryAllocator()
cdef int* label = <int*>mem.allocarray(n, sizeof(int))
cdef int* alpha = <int*>mem.allocarray(n, sizeof(int))
Expand Down Expand Up @@ -1237,7 +1269,8 @@ def lex_M_fast(G, triangulation=False, initial_vertex=None):
k += 2
label[w] = k

free_short_digraph(sd)
if not isinstance(G, StaticSparseBackend):
free_short_digraph(sd)

cdef list ordering = [int_to_v[alpha[i]] for i in range(n)]

Expand Down Expand Up @@ -1354,9 +1387,9 @@ def maximum_cardinality_search(G, reverse=False, tree=False, initial_vertex=None
sage: G.maximum_cardinality_search(initial_vertex=0)
[3, 2, 1, 0]
sage: G.maximum_cardinality_search(initial_vertex=1)
[0, 3, 2, 1]
[3, 2, 0, 1]
sage: G.maximum_cardinality_search(initial_vertex=2)
[0, 1, 3, 2]
[0, 3, 1, 2]
sage: G.maximum_cardinality_search(initial_vertex=3)
[0, 1, 2, 3]
sage: G.maximum_cardinality_search(initial_vertex=3, reverse=True)
Expand Down Expand Up @@ -1388,6 +1421,17 @@ def maximum_cardinality_search(G, reverse=False, tree=False, initial_vertex=None
Traceback (most recent call last):
...
ValueError: vertex (17) is not a vertex of the graph

Immutable graphs;:

sage: G = graphs.RandomGNP(10, .7)
sage: G._backend
<sage.graphs.base.sparse_graph.SparseGraphBackend ...>
sage: H = Graph(G, immutable=True)
sage: H._backend
<sage.graphs.base.static_sparse_backend.StaticSparseBackend ...>
sage: G.maximum_cardinality_search() == H.maximum_cardinality_search()
True
"""
if tree:
from sage.graphs.digraph import DiGraph
Expand All @@ -1398,17 +1442,27 @@ def maximum_cardinality_search(G, reverse=False, tree=False, initial_vertex=None
if N == 1:
return (list(G), DiGraph(G)) if tree else list(G)

cdef list int_to_vertex = list(G)
cdef list int_to_vertex
cdef StaticSparseCGraph cg
cdef short_digraph sd
if isinstance(G, StaticSparseBackend):
cg = <StaticSparseCGraph> G._cg
sd = <short_digraph> cg.g
int_to_vertex = cg._vertex_to_labels
else:
int_to_vertex = list(G)
init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_vertex)

if initial_vertex is None:
initial_vertex = 0
elif initial_vertex in G:
initial_vertex = int_to_vertex.index(initial_vertex)
if isinstance(G, StaticSparseBackend):
initial_vertex = cg._vertex_to_int[initial_vertex]
else:
initial_vertex = int_to_vertex.index(initial_vertex)
else:
raise ValueError("vertex ({0}) is not a vertex of the graph".format(initial_vertex))

cdef short_digraph sd
init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_vertex)
cdef uint32_t** p_vertices = sd.neighbors
cdef uint32_t* p_tmp
cdef uint32_t* p_end
Expand All @@ -1420,27 +1474,18 @@ def maximum_cardinality_search(G, reverse=False, tree=False, initial_vertex=None

cdef int i, u, v
for i in range(N):
weight[i] = 0
seen[i] = False
pred[i] = i

# We emulate a heap with decrease key operation using a priority queue.
# A vertex can be inserted multiple times (up to its degree), but only the
# first extraction (with maximum weight) matters. The size of the queue will
# never exceed O(m).
cdef priority_queue[pair[int, int]] pq
pq.push((0, initial_vertex))
# We emulate a max-heap data structure using a min-heap with negative values
cdef PairingHeap_of_n_integers P = PairingHeap_of_n_integers(N)
P.push(initial_vertex, 0)

# The ordering alpha is feed in reversed order and revert afterword
cdef list alpha = []

while not pq.empty():
_, u = pq.top()
pq.pop()
if seen[u]:
# We use a lazy decrease key mode, so u can be several times in pq
continue

while P:
u = P.top_item()
P.pop()
alpha.append(int_to_vertex[u])
seen[u] = True

Expand All @@ -1450,12 +1495,13 @@ def maximum_cardinality_search(G, reverse=False, tree=False, initial_vertex=None
v = p_tmp[0]
if not seen[v]:
weight[v] += 1
pq.push((weight[v], v))
P.decrease(v, -weight[v])
if pred[v] == v:
pred[v] = u
p_tmp += 1

free_short_digraph(sd)
if not isinstance(G, StaticSparseBackend):
free_short_digraph(sd)

if len(alpha) < N:
raise ValueError("the input graph is not connected")
Expand Down Expand Up @@ -1762,16 +1808,18 @@ def maximum_cardinality_search_M(G, initial_vertex=None):
Traceback (most recent call last):
...
ValueError: vertex (17) is not a vertex of the graph
"""
cdef list int_to_vertex = list(G)

if initial_vertex is None:
initial_vertex = 0
elif initial_vertex in G:
initial_vertex = int_to_vertex.index(initial_vertex)
else:
raise ValueError("vertex ({0}) is not a vertex of the graph".format(initial_vertex))
Immutable graphs::

sage: G = graphs.RandomGNP(10, .7)
sage: G._backend
<sage.graphs.base.sparse_graph.SparseGraphBackend ...>
sage: H = Graph(G, immutable=True)
sage: H._backend
<sage.graphs.base.static_sparse_backend.StaticSparseBackend ...>
sage: G.maximum_cardinality_search_M() == H.maximum_cardinality_search_M()
True
"""
cdef int N = G.order()
if not N:
return ([], [], [])
Expand All @@ -1781,8 +1829,26 @@ def maximum_cardinality_search_M(G, initial_vertex=None):
# Copying the whole graph to obtain the list of neighbors quicker than by
# calling out_neighbors. This data structure is well documented in the
# module sage.graphs.base.static_sparse_graph
cdef list int_to_vertex
cdef StaticSparseCGraph cg
cdef short_digraph sd
init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_vertex)
if isinstance(G, StaticSparseBackend):
cg = <StaticSparseCGraph> G._cg
sd = <short_digraph> cg.g
int_to_vertex = cg._vertex_to_labels
else:
int_to_vertex = list(G)
init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_vertex)

if initial_vertex is None:
initial_vertex = 0
elif initial_vertex in G:
if isinstance(G, StaticSparseBackend):
initial_vertex = cg._vertex_to_int[initial_vertex]
else:
initial_vertex = int_to_vertex.index(initial_vertex)
else:
raise ValueError("vertex ({0}) is not a vertex of the graph".format(initial_vertex))

cdef MemoryAllocator mem = MemoryAllocator()
cdef int* alpha = <int*>mem.calloc(N, sizeof(int))
Expand All @@ -1794,7 +1860,8 @@ def maximum_cardinality_search_M(G, initial_vertex=None):
maximum_cardinality_search_M_short_digraph(sd, initial_vertex, alpha, alpha_inv, F, X)
sig_off()

free_short_digraph(sd)
if not isinstance(G, StaticSparseBackend):
free_short_digraph(sd)

cdef int u, v
return ([int_to_vertex[alpha[u]] for u in range(N)],
Expand Down
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