def test_returns_hyperpath_containing_source_if_source_equals_destination(
self):
s = '1'
T = {s: None}
H = DirectedHypergraph()
H.add_node(s)
path = directed_paths.get_hyperpath_from_predecessors(H, T, s, s)
self.assertTrue(path.has_node(s))
def test_returns_hyperpath_containing_source_if_source_equals_destination(
self):
s = '1'
T = {s: None}
H = DirectedHypergraph()
H.add_node(s)
path = directed_paths.get_hyperpath_from_predecessors(H, T, s, s)
self.assertTrue(path.has_node(s))
def test_returns_hyperpath_with_single_node_if_source_equals_destination(
self):
s = '1'
T = {s: None}
H = DirectedHypergraph()
H.add_node(s)
path = directed_paths.get_hyperpath_from_predecessors(H, T, s, s)
self.assertEqual(len(path.get_node_set()), 1)
self.assertEqual(len(path.get_hyperedge_id_set()), 0)
def test_returns_hyperpath_with_single_node_if_source_equals_destination(
self):
s = '1'
T = {s: None}
H = DirectedHypergraph()
H.add_node(s)
path = directed_paths.get_hyperpath_from_predecessors(H, T, s, s)
self.assertEqual(len(path.get_node_set()), 1)
self.assertEqual(len(path.get_hyperedge_id_set()), 0)
def test_returns_hyperpath_for_simple_tree(self):
s1, s2, s3, s4 = 1, 2, 3, 4
H = DirectedHypergraph()
H.add_nodes([s1, s2, s3, s4])
e1 = H.add_hyperedge([s1], [s2])
e2 = H.add_hyperedge([s1], [s3])
e3 = H.add_hyperedge([s3], [s4])
T = {s4: e3, s3: e2, s2: e1, s1: None}
path = directed_paths.get_hyperpath_from_predecessors(H, T, s1, s4)
# validate nodes
self.assertEqual(path.get_node_set(), {s1, s3, s4})
# validate hyperedges
self.assertEqual(len(path.get_hyperedge_id_set()), 2)
self.assertTrue(path.get_hyperedge_id([1], [3]))
self.assertTrue(path.get_hyperedge_id([3], [4]))
def test_returns_hyperpath_for_simple_tree(self):
s1, s2, s3, s4 = 1, 2, 3, 4
H = DirectedHypergraph()
H.add_nodes([s1, s2, s3, s4])
e1 = H.add_hyperedge([s1], [s2])
e2 = H.add_hyperedge([s1], [s3])
e3 = H.add_hyperedge([s3], [s4])
T = {s4: e3, s3: e2, s2: e1, s1: None}
path = directed_paths.get_hyperpath_from_predecessors(H, T, s1, s4)
# validate nodes
self.assertEqual(path.get_node_set(), {s1, s3, s4})
# validate hyperedges
self.assertEqual(len(path.get_hyperedge_id_set()), 2)
self.assertTrue(path.get_hyperedge_id([1], [3]))
self.assertTrue(path.get_hyperedge_id([3], [4]))
def test_returns_hyperpath_when_node_is_in_tail_of_two_edges(self):
s1, s2, s3 = 1, 2, 3
s4 = 4
H = DirectedHypergraph()
e1 = H.add_hyperedge([s1], [s2])
e2 = H.add_hyperedge([s2], [s3])
e3 = H.add_hyperedge([s2, s3], [s4])
T = {s4: e3, s3: e2, s2: e1, s1: None}
path = directed_paths.get_hyperpath_from_predecessors(H, T, s1, s4)
# validate nodes
self.assertEqual(path.get_node_set(), {s1, s2, s3, s4})
# validate hyperedges
self.assertEqual(len(path.get_hyperedge_id_set()), 3)
self.assertTrue(path.get_hyperedge_id([2, 3], [4]))
self.assertTrue(path.get_hyperedge_id([2], [3]))
self.assertTrue(path.get_hyperedge_id([1], [2]))
def test_returns_hyperpath_when_node_is_in_tail_of_two_edges(self):
s1, s2, s3 = 1, 2, 3
s4 = 4
H = DirectedHypergraph()
e1 = H.add_hyperedge([s1], [s2])
e2 = H.add_hyperedge([s2], [s3])
e3 = H.add_hyperedge([s2, s3], [s4])
T = {s4: e3, s3: e2, s2: e1, s1: None}
path = directed_paths.get_hyperpath_from_predecessors(H, T, s1, s4)
# validate nodes
self.assertEqual(path.get_node_set(), {s1, s2, s3, s4})
# validate hyperedges
self.assertEqual(len(path.get_hyperedge_id_set()), 3)
self.assertTrue(path.get_hyperedge_id([2, 3], [4]))
self.assertTrue(path.get_hyperedge_id([2], [3]))
self.assertTrue(path.get_hyperedge_id([1], [2]))
def test_returns_hyperpath_for_tree_with_multiple_nodes_in_tail(self):
s1, s2, s3 = 1, 2, 3
s4, s5, s6 = 4, 5, 6
H = DirectedHypergraph()
H.add_nodes([s1, s2, s3, s4, s5, s6])
e1 = H.add_hyperedge([s1], [s2])
e2 = H.add_hyperedge([s1], [s3])
e3 = H.add_hyperedge([s1], [s4])
e4 = H.add_hyperedge([s2, s3], [s5])
e5 = H.add_hyperedge([s5], [s6])
T = {s6: e5, s5: e4, s4: e3, s3: e2, s2: e1, s1: None}
path = directed_paths.get_hyperpath_from_predecessors(H, T, s1, s6)
# validate nodes
self.assertEqual(path.get_node_set(), {s1, s2, s3, s5, s6})
# validate hyperedges
self.assertEqual(len(path.get_hyperedge_id_set()), 4)
self.assertTrue(path.get_hyperedge_id([5], [6]))
self.assertTrue(path.get_hyperedge_id([2, 3], [5]))
self.assertTrue(path.get_hyperedge_id([1], [3]))
self.assertTrue(path.get_hyperedge_id([1], [2]))
def test_returns_hyperpath_for_tree_with_multiple_nodes_in_tail(self):
s1, s2, s3 = 1, 2, 3
s4, s5, s6 = 4, 5, 6
H = DirectedHypergraph()
H.add_nodes([s1, s2, s3, s4, s5, s6])
e1 = H.add_hyperedge([s1], [s2])
e2 = H.add_hyperedge([s1], [s3])
e3 = H.add_hyperedge([s1], [s4])
e4 = H.add_hyperedge([s2, s3], [s5])
e5 = H.add_hyperedge([s5], [s6])
T = {s6: e5, s5: e4, s4: e3, s3: e2, s2: e1, s1: None}
path = directed_paths.get_hyperpath_from_predecessors(H, T, s1, s6)
# validate nodes
self.assertEqual(path.get_node_set(), {s1, s2, s3, s5, s6})
# validate hyperedges
self.assertEqual(len(path.get_hyperedge_id_set()), 4)
self.assertTrue(path.get_hyperedge_id([5], [6]))
self.assertTrue(path.get_hyperedge_id([2, 3], [5]))
self.assertTrue(path.get_hyperedge_id([1], [3]))
self.assertTrue(path.get_hyperedge_id([1], [2]))
def k_shortest_hyperpaths(H, source_node, destination_node, k, F=sum_function):
"""Computes the k shortest hyperpaths from a source node to every other
node in the hypergraph.
This algorithm is only applicable to directed B-hypergraphs.
The algorithm is described in the paper:
Lars Relund Nielsen, Kim Allan Andersen, Daniele Pretolani,
Finding the K shortest hyperpaths, Computers & Operations Research,
Volume 32, Issue 6, June 2005, Pages 1477-1497, ISSN 0305-0548,
http://dx.doi.org/10.1016/j.cor.2003.11.014.
(http://www.sciencedirect.com/science/article/pii/S0305054803003459)
:param H: the hypergraph for which the function will compute the shortest
hyperpaths.
:param source_node: the source node in H for the path computation.
:param destination_node: the destination node in H for the path
computation.
:param k: a positive integer indicating how many paths to compute.
:param F: [optional] function used for the shortest path computation.
See algorithms.directed_paths module for expected format of
function.
:returns: a list containing at most k hyperpaths (DirectedHypergraph) from
source to destination in ascending order of path length.
:raises: TypeError -- Input hypergraph must be a B-hypergraph
:raises: TypeError -- Algorithm only applicable to directed hypergraphs
:raises: ValueError -- source_node must be a node in H
:raises: ValueError -- destination_node must be a node in H
:raises: TypeError -- k must be an integer
:raises: ValueError -- k must be a positive integer
"""
try:
if not H.is_B_hypergraph():
raise TypeError("Input graph must be a B-hypergraph")
except AttributeError:
raise TypeError("Algorithm only applicable to directed hypergraphs")
if not H.has_node(source_node):
raise ValueError("source_node must be a node in H. \
%s received" % source_node)
if not H.has_node(destination_node):
raise ValueError("destination_node must be a node in H. \
%s received" % destination_node)
if type(k) != int:
raise TypeError("k must be an integer. %s received" % k)
if k <= 0:
raise ValueError("k must be a positive integer. %s received" % k)
# Container for the k-shortest hyperpaths
paths = []
# Container for the candidate paths. Every item is a 4-tuple:
# 1) subgraph H'
# 2) lower bound on shortest hyperpath weight
# 3) predecessor function of shortest hypertree rootes at s on H'
# 4) valid ordering of the nodes in H'
candidates = []
shortest_hypertree, W, ordering = \
shortest_b_tree(H, source_node, F=F, valid_ordering=True)
# Check if there is source-destination hyperpath
# if there isn't the for loop below
# will break immediately and the function returns an empty list
if W[destination_node] != float('inf'):
candidates.append((H, W, shortest_hypertree, ordering))
i = 1
while i <= k and candidates:
ind = candidates.index(
min(candidates, key=lambda x: x[1][destination_node]))
kShortest = candidates[ind]
if kShortest[2]:
candidates.pop(ind)
path = \
get_hyperpath_from_predecessors(kShortest[0], kShortest[2],
source_node, destination_node)
pathPredecessor = \
{node: edge for node, edge in kShortest[2].items()
if node in path.get_node_set()}
pathOrdering = \
[node for node in kShortest[3] if node in pathPredecessor]
paths.append(path)
# check if we are done
if len(paths) == k:
break
branches = _branching_step(kShortest[0], pathPredecessor,
pathOrdering)
for j, branch in enumerate(branches):
lb = _compute_lower_bound(branch, j, kShortest[2],
pathOrdering, kShortest[1],
destination_node, F)
if lb < float('inf'):
candidates.append((branch,
{destination_node: lb},
None, None))
i += 1
else:
# Compute shortest hypertree for kShortest[0] and exact bound
# reinsert into candidates
H_sub = kShortest[0]
tree_sub, W_sub, ordering_sub = \
shortest_b_tree(H_sub, source_node, valid_ordering=True)
candidates[ind] = (H_sub, W_sub, tree_sub, ordering_sub)
return paths
