def test_correctness():
# note: in the future can restrict all graphs to have the same number of nodes, for analysis
graphs = [lambda: basic_graph(), lambda: complete_graph(10), lambda: balanced_tree(3, 5), lambda: barbell_graph(6, 7),
lambda: binomial_tree(10), lambda: cycle_graph(50),
lambda: path_graph(200), lambda: star_graph(200)]
names = ["basic_graph", "complete_graph", "balanced_tree", "barbell_graph", "binomial_tree", "cycle_graph",
"path_graph", "star_graph"]
for graph, name in zip(graphs, names):
print(f"Testing graph {name}...")
# Initialize both graphs
G_dinitz = graph()
G_gr = graph()
# Set random capacities of graph edges
for u, v in G_dinitz.edges:
cap = randint(1, 20)
G_dinitz.edges[u, v]["capacity"] = cap
G_gr.edges[u, v]["capacity"] = cap
# Pick random start and end node
start_node = randint(0, len(G_dinitz.nodes)-1)
end_node = randint(0, len(G_dinitz.nodes)-1)
while start_node == end_node: end_node = randint(0, len(G_dinitz.nodes)-1)
# Run max-flow
R_dinitz = dinitz(G_dinitz, start_node, end_node)
R_gr = goldberg_rao(G_gr, start_node, end_node)
# Check correctness
d_mf = R_dinitz.graph["flow_value"]
gr_mf = R_gr.graph["flow_value"]
assert d_mf == gr_mf, f"Computed max flow in {name} graph is {d_mf}, but goldberg_rao function computed {gr_mf}"
def run_analysis_n_nodes(n, unit_cap, n_runs=1):
print(f"Running analysis for {n} nodes...")
graphs = [lambda: complete_graph(n)]
results_gr = {}
results_dinitz = {}
for graph, name in zip(graphs, names):
# Initialize both graphs
G_dinitz = graph()
G_gr = G_dinitz.copy()
total_time_gr = 0
total_time_dinitz = 0
for _ in range(n_runs):
# Set random capacities of graph edges
for u, v in G_dinitz.edges:
cap = randint(1, 100) if not unit_cap else 1
G_dinitz.edges[u, v]["capacity"] = cap
G_gr.edges[u, v]["capacity"] = cap
# Pick random start and end node
start_node = randint(0, len(G_dinitz.nodes) - 1)
end_node = randint(0, len(G_dinitz.nodes) - 1)
while start_node == end_node:
end_node = randint(0, len(G_dinitz.nodes) - 1)
# Run max-flow
init_time = time.time()
R_dinitz = dinitz(G_dinitz, start_node, end_node)
total_time_dinitz += time.time() - init_time
init_time = time.time()
R_gr = goldberg_rao(G_gr, start_node, end_node)
total_time_gr += time.time() - init_time
# Check correctness
d_mf = R_dinitz.graph["flow_value"]
gr_mf = R_gr.graph["flow_value"]
if d_mf != gr_mf:
vprint(
f"\t\t\tComputed max flow in {name} graph is {d_mf}, but goldberg_rao function computed {gr_mf}"
.upper())
vprint(
f"{name} with {n} nodes took {total_time_gr / n_runs} seconds with goldberg_rao"
)
vprint(
f"{name} with {n} nodes took {total_time_dinitz / n_runs} seconds with dinitz"
)
results_gr[name] = total_time_gr / n_runs
results_dinitz[name] = total_time_dinitz / n_runs
return results_gr, results_dinitz
def run_analysis_n_nodes(n, unit_cap, n_runs=3):
print(f"Running analysis for {n} nodes...")
graphs = [
lambda: balanced_tree(2, int(round(np.log2(n) - 1))),
lambda: binomial_tree(int(round(np.log2(n)))), lambda: cycle_graph(n),
lambda: path_graph(n), lambda: star_graph(n - 1),
lambda: random_regular_graph(3, n), lambda: random_regular_graph(5, n)
]
results_dinitz = {}
for graph, name in zip(graphs, names):
# Initialize both graphs
G_dinitz = graph()
total_time_dinitz = 0
for _ in range(n_runs):
# Set random capacities of graph edges
for u, v in G_dinitz.edges:
cap = randint(1, 100) if not unit_cap else 1
G_dinitz.edges[u, v]["capacity"] = cap
# Pick random start and end node
start_node = randint(0, len(G_dinitz.nodes) - 1)
end_node = randint(0, len(G_dinitz.nodes) - 1)
while start_node == end_node:
end_node = randint(0, len(G_dinitz.nodes) - 1)
# Run max-flow
init_time = time.time()
R_dinitz = dinitz(G_dinitz, start_node, end_node)
total_time_dinitz += time.time() - init_time
vprint(
f"{name} with {len(G_dinitz.nodes)} nodes took {total_time_dinitz / n_runs} seconds with dinitz"
)
results_dinitz[name] = total_time_dinitz / n_runs
return results_dinitz
def Din(G, a, b):
start_time = time()
R = dinitz(G, a, b)
time_elapsed = time() - start_time
return time_elapsed