def edge_disjoint_shortest_pair(g, src, dst):
'''Return list of two edge-disjoint paths w/shortest total cost.
@param g: NetworkX Graph object
@param src: src node label
@param dst: dst node label
@param paths: two-element list of path lists, arbitrary ordering
'''
# 1. Use BFS to get shortest path.
shortest_path = BFS(g, src, dst)
# 2. Replace each edge of the shortest path (equivalent to two oppositely
# directed arcs) by a single arc directed toward the source vertex.
# 3. Make the length of each of the above arcs negative.
g2 = flip_and_negate_path(g, shortest_path)
# 4. Run the modified Dijkstra or the BFS algorithm again and from the
# source vertex to the destination vertex in the above modified graph.
shortest_path_2 = BFS(g2, src, dst)
first_pathtotal = pathlen(g, shortest_path) + pathlen(g2, shortest_path_2)
# 5. Transform to the original graph, and erase any interlacing edges of
# the two paths found. Group the remaining edges to obtain the shortest
# pair of edge-disjoint paths.
path1, path2 = grouped_shortest_pair(g, shortest_path, shortest_path_2)
path1len = pathlen(g, path1)
path2len = pathlen(g, path2)
second_pathtotal = path1len + path2len
assert (first_pathtotal == second_pathtotal)
return [path1, path2]
def edge_disjoint_shortest_pair(g, src, dst):
'''Return list of two edge-disjoint paths w/shortest total cost.
@param g: NetworkX Graph object
@param src: src node label
@param dst: dst node label
@param paths: two-element list of path lists, arbitrary ordering
'''
# 1. Use BFS to get shortest path.
shortest_path = BFS(g, src, dst)
# 2. Replace each edge of the shortest path (equivalent to two oppositely
# directed arcs) by a single arc directed toward the source vertex.
# 3. Make the length of each of the above arcs negative.
g2 = flip_and_negate_path(g, shortest_path)
# 4. Run the modified Dijkstra or the BFS algorithm again and from the
# source vertex to the destination vertex in the above modified graph.
shortest_path_2 = BFS(g2, src, dst)
first_pathtotal = pathlen(g, shortest_path) + pathlen(g2, shortest_path_2)
# 5. Transform to the original graph, and erase any interlacing edges of
# the two paths found. Group the remaining edges to obtain the shortest
# pair of edge-disjoint paths.
path1, path2 = grouped_shortest_pair(g, shortest_path, shortest_path_2)
path1len = pathlen(g, path1)
path2len = pathlen(g, path2)
second_pathtotal = path1len + path2len
assert(first_pathtotal == second_pathtotal)
return [path1, path2]
def test_example_3_13_a_mod_2(self):
'''Example 3.13a on pg 65, mod on pg 78.
This example has two equally good path choices, so only check sum of
paths.
'''
g = graph_fig_3_13_a_mod_2
ed_paths = edge_disjoint_shortest_pair(g, 'A', 'Z')
ed_paths_len = sum([pathlen(g, ed_paths[i]) for i in [0, 1]])
exp_paths = [[i for i in 'ABCDEFZ'], [i for i in 'AGDHZ']]
exp_paths_len = sum([pathlen(g, exp_paths[i]) for i in [0, 1]])
self.assertEqual(ed_paths_len, exp_paths_len)
def test_example_3_13_a_mod_2(self):
'''Example 3.13a on pg 65, mod on pg 78.
This example has two equally good path choices, so only check sum of
paths.
'''
g = graph_fig_3_13_a_mod_2
ed_paths = edge_disjoint_shortest_pair(g, 'A', 'Z')
ed_paths_len = sum([pathlen(g, ed_paths[i]) for i in [0, 1]])
exp_paths = [[i for i in 'ABCDEFZ'], [i for i in 'AGDHZ']]
exp_paths_len = sum([pathlen(g, exp_paths[i]) for i in [0, 1]])
self.assertEqual(ed_paths_len, exp_paths_len)
def test_example_3_13_a_mod_2(self):
'''Example 3.13a on pg 65, mod 2 on pg 78.
This example has two equally good path choices (ABIFZ / AGDHZ and
ABCDEFZ / AGDHZ), so only check sum of paths.
'''
g = graph_fig_3_13_a_mod_2
vd_paths = vertex_disjoint_shortest_pair(g, 'A', 'Z')
vd_paths_len = sum([pathlen(g, vd_paths[i]) for i in [0, 1]])
exp_paths = [[i for i in 'ABIFZ'], [i for i in 'AGDHZ']]
exp_paths_len = sum([pathlen(g, exp_paths[i]) for i in [0, 1]])
compare_path_lists(self, vd_paths, exp_paths, g, 14)
self.assertEqual(vd_paths_len, exp_paths_len)
def test_example_3_13_a_mod_2(self):
'''Example 3.13a on pg 65, mod 2 on pg 78.
This example has two equally good path choices (ABIFZ / AGDHZ and
ABCDEFZ / AGDHZ), so only check sum of paths.
'''
g = graph_fig_3_13_a_mod_2
vd_paths = vertex_disjoint_shortest_pair(g, 'A', 'Z')
vd_paths_len = sum([pathlen(g, vd_paths[i]) for i in [0, 1]])
exp_paths = [[i for i in 'ABIFZ'], [i for i in 'AGDHZ']]
exp_paths_len = sum([pathlen(g, exp_paths[i]) for i in [0, 1]])
compare_path_lists(self, vd_paths, exp_paths, g, 14)
self.assertEqual(vd_paths_len, exp_paths_len)
def compare_path_lists(test, one, two, g = None, total = None):
'''Compare two path lists.
Useful because shortest path algorithms yield paths in arbitrary orders.
@param test: instance of unittest.TestCase
@param one: list of path nodes
@param two: list of path nodes
@param g: optional NetworkX graph for path length verification
@param total: optional total length of both paths
'''
def make_tuple_set(path_list):
return set([tuple(path) for path in path_list])
test.assertEqual(make_tuple_set(one), make_tuple_set(two))
if g:
test.assertEqual(total, pathlen(g, one[0]) + pathlen(g, one[1]))
def compare_path_lists(test, one, two, g=None, total=None):
'''Compare two path lists.
Useful because shortest path algorithms yield paths in arbitrary orders.
@param test: instance of unittest.TestCase
@param one: list of path nodes
@param two: list of path nodes
@param g: optional NetworkX graph for path length verification
@param total: optional total length of both paths
'''
def make_tuple_set(path_list):
return set([tuple(path) for path in path_list])
test.assertEqual(make_tuple_set(one), make_tuple_set(two))
if g:
test.assertEqual(total, pathlen(g, one[0]) + pathlen(g, one[1]))
def test_example_3_16_a(self):
'''Example 3.16a on pg 74.'''
g = graph_fig_3_16_a
path = BFS(g, 'A', 'Z')
self.assertEqual(path, [i for i in 'ABCDEFZ'])
self.assertEqual(pathlen(g, path), 6)
def test_example_3_1_a(self):
'''Example 3.1a on pg. 41.'''
g = graph_fig_3_1_a
path = BFS(g, 'A', 'Z')
self.assertEqual(path, [i for i in 'ABCDZ'])
self.assertEqual(pathlen(g, path), 4)
def test_example_2_6(self):
'''Example 2.6 on pg. 35.'''
g = graph_fig_2_3
path = BFS(g, 'A', 'Z')
self.assertEqual(path, [i for i in 'ADECBZ'])
self.assertEqual(pathlen(g, path), 12)
def test_example_3_16_a(self):
'''Example 3.16a on pg 74.'''
g = graph_fig_3_16_a
path = BFS(g, 'A', 'Z')
self.assertEqual(path, [i for i in 'ABCDEFZ'])
self.assertEqual(pathlen(g, path), 6)
def test_example_3_1_a(self):
'''Example 3.1a on pg. 41.'''
g = graph_fig_3_1_a
path = BFS(g, 'A', 'Z')
self.assertEqual(path, [i for i in 'ABCDZ'])
self.assertEqual(pathlen(g, path), 4)
def test_example_2_6(self):
'''Example 2.6 on pg. 35.'''
g = graph_fig_2_3
path = BFS(g, 'A', 'Z')
self.assertEqual(path, [i for i in 'ADECBZ'])
self.assertEqual(pathlen(g, path), 12)
