1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
|
###########################
# TODO
# output paths
# visualization?
# algorithms:
# beam search
# best-first
# kbest
# kruskal (MST)?
# transitive closure?
###########################
require 'json'
module DAG
class DAG::Node
attr_accessor :label, :edges, :incoming, :score, :mark
def initialize label=nil, edges=[], incoming=[], score=nil
@label = label
@edges = edges # outgoing
@incoming = incoming
@score = nil
end
def add_edge head, weight=0
exit if self==head # no self-cycles!
@edges << DAG::Edge.new(self, head, weight)
return @edges.last
end
def to_s
"DAG::Node<label:#{label}, edges:#{edges.size}, incoming:#{incoming.size}>"
end
def repr
"#{to_s} #{@score} out:#{@edges} in:[#{@incoming.map{|e| e.to_s}.join ', '}]"
end
end
class DAG::Edge
attr_accessor :tail, :head, :weight, :mark
def initialize tail=nil, head=nil, weight=0
@tail = tail
@head = head
@weight = weight
@mark = false # did we already follow this edge? -- for topological sorting
end
def to_s
s = "DAG::Edge<#{@tail} ->[#{weight}] #{@head}"
s += " x" if @mark
s += ">"
s
end
end
# depth-first search
# w/o markings as we do not have cycles
def DAG::dfs n, target_label
return n if n.label==target_label # assumes uniq labels!
stack = n.edges.map { |i| i.head }
while !stack.empty?
m = stack.pop
return DAG::dfs m, target_label
end
return nil
end
# breadth-first search
# w/o markings as we do not have cycles
def DAG::bfs n, target_label
queue = [n]
while !queue.empty?
m = queue.shift
return m if m.label==target_label
m.edges.each { |e| queue << e.head }
end
return nil
end
# topological sort
def DAG::topological_sort graph
sorted = []
s = graph.reject { |n| !n.incoming.empty? }
while !s.empty?
sorted << s.shift
sorted.last.edges.each { |e|
e.mark = true
s << e.head if e.head.incoming.reject{|f| f.mark}.empty?
}
end
return sorted
end
# initialize graph scores with semiring One
def DAG::init graph, semiring, source_node
graph.each {|n| n.score=semiring.null}
source_node.score = semiring.one
end
# viterbi
def DAG::viterbi graph, semiring=ViterbiSemiring, source_node
toposorted = DAG::topological_sort(graph)
DAG::init(graph, semiring, source_node)
toposorted.each { |n|
n.incoming.each { |e|
# update
n.score = \
semiring.add.call(n.score, \
semiring.multiply.call(e.tail.score, e.weight)
)
}
}
end
# forward viterbi
def DAG::viterbi_forward graph, semiring=ViterbiSemiring, source_node
toposorted = DAG::topological_sort(graph)
DAG::init(graph, semiring, source_node)
toposorted.each { |n|
n.edges.each { |e|
e.head.score = \
semiring.add.call(e.head.score, \
semiring.multiply.call(n.score, e.weight)
)
}
}
end
# Dijkstra algorithm
# for A*-search we would need an optimistic estimate of
# future cost at each node
def DAG::dijkstra graph, semiring=RealSemiring.new, source_node
DAG::init(graph, semiring, source_node)
q = PriorityQueue.new graph
while !q.empty?
n = q.pop
n.edges.each { |e|
e.head.score = \
semiring.add.call(e.head.score, \
semiring.multiply.call(n.score, e.weight))
q.sort!
}
end
end
# Bellman-Ford algorithm
def DAG::bellman_ford(graph, semiring=RealSemiring.new, source_node)
DAG::init(graph, semiring, source_node)
edges = []
graph.each { |n| edges |= n.edges }
# relax edges
(graph.size-1).times{ |i|
edges.each { |e|
e.head.score = \
semiring.add.call(e.head.score, \
semiring.multiply.call(e.tail.score, e.weight))
}
}
# we do not allow cycles (negative or positive)
end
# Floyd algorithm
def DAG::floyd(graph, semiring=nil)
dist_matrix = []
graph.each_index { |i|
dist_matrix << []
graph.each_index { |j|
val = 1.0/0.0
val = 0.0 if i==j
dist_matrix.last << val
}
}
edges = []
graph.each { |n| edges |= n.edges }
edges.each { |e|
dist_matrix[graph.index(e.tail)][graph.index(e.head)] = e.weight
}
0.upto(graph.size-1) { |k|
0.upto(graph.size-1) { |i|
0.upto(graph.size-1) { |j|
if dist_matrix[i][k] + dist_matrix[k][j] < dist_matrix[i][j]
dist_matrix [i][j] = dist_matrix[i][k] + dist_matrix[k][j]
end
}
}
}
return dist_matrix
end
# returns a list of nodes (graph) and a hash for finding
# nodes by their label (these need to be unique!)
def DAG::read_graph_from_json fn, semiring=RealSemiring.new
graph = []
nodes_by_label = {}
h = JSON.parse File.new(fn).read
h['nodes'].each { |i|
n = DAG::Node.new i['label']
graph << n
nodes_by_label[n.label] = n
}
h['edges'].each { |i|
n = nodes_by_label[i['tail']]
a = n.add_edge(nodes_by_label[i['head']], semiring.convert.call(i['weight'].to_f))
nodes_by_label[i['head']].incoming << a
}
return graph, nodes_by_label
end
end # module
|
