[graph-tool] dfs/bfs seem to have overhead depending on total graph size
My-Tien Nguyen
my-tien at mailbox.org
Fri Feb 26 12:08:31 CET 2021
Hi all,
I’ve got a very large undirected graph (407 mil vertices, 522 mil edges,
2 vertex properties) that consists of multiple connected components (ccs).
I noticed that when I call e.g. dfs_iterator or dfs_search on a source
vertex, it takes around 1 – 2 seconds to return. The upper bound is
depending on the component’s size, but the lower bound seems to be the
same for all components.
I have created a test graph with only a subset of the ccs of the large
graph. Iterating the same cc in the test graph takes only a couple of
milliseconds instead of ≥ 1 s. This tells me, that the dfs/bfs iterators
have some kind of overhead depending on the complete graph size.
I wrote a DFSVisitor that collects some timings during iteration to
better see which steps consume time. Here are the results (rounded for
readability):
In [30]: test_dfs(graph, graph.vertex(0))
# first time the function is entered
visitor.start_vertex_t 2.3e-05 s
visitor.first_discover_vertex_t 0.18 s
visitor.first_examine_edge_t 0.18 s
visitor.first_tree_edge_t 0.63 s
visitor.first_finish_vertex_t 0.63 s
# average time between last 2 calls of the function
visitor.discover_vertex_t 0.002 s
visitor.examine_edge_t 0.001 s
visitor.tree_edge_t 0.001 s
visitor.finish_vertex_t 0.001 s
# last time finished() is called
visitor.finished 1.3 s
# number of times the functions were called
visitor.discovered_vertices 565
visitor.examined_edges 1978
visitor.tree_edges 564
visitor.finished_vertices 565
took 1.38 s
As you can see, start_vertex is called immediately, but then it takes a
very long time until the other Visitor functions are called for the
first time after which the calls are faster again, but still quite slow.
On the test graph I think I can see the same trend with smaller numbers
because the graph is smaller:
In [30]: test_dfs(test_graph, test_graph.vertex(0))
# first time the function is entered
visitor.start_vertex_t 2e-05 s
visitor.first_discover_vertex_t 0.0007 s
visitor.first_examine_edge_t 0.0007 s
visitor.first_tree_edge_t 0.0016s
visitor.first_finish_vertex_t 0.0015 s
# average time between last 2 calls of the function
visitor.discover_vertex_t 1.6e-05 s
visitor.examine_edge_t 3.7e-06 s
visitor.tree_edge_t 1.4e-05 s
visitor.finish_vertex_t 1.4e-05 s
# last time finished() is called
visitor.finished 0.01 s
# number of times the functions were called
visitor.discovered_vertices 565
visitor.examined_edges 1978
visitor.tree_edges 564
visitor.finished_vertices 565
took 0.01 s
If I iterate the same cc in the large graph in python, it takes me only
a couple of milliseconds:
def dfs(graph, vertex_idx):
t = time.time()
todo = {vertex_idx}
visited = set()
while len(todo) > 0:
next_vertex = todo.pop()
visited.add(next_vertex)
todo |=
set(graph.iter_all_neighbors(graph.vertex(next_vertex))) - visited
print(f'dfs took {time.time() - t} s')
return visited
In [38]: d = dfs(graph, 0)
dfs took 0.01653146743774414 s
Because of graph_tool’s slowness for small ccs I ended up writing a
heuristic that always attempts a naive python dfs first, but aborts if 1
second is exceeded and only then does the graph_tool dfs. Anyone know
what’s going on here?
Best
My-Tien
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