Merge: lib/graphs: introduce PageRank computation on digraphs

Implement famous Google's `PageRank` algorithm for directed graphs.

Ping @ablondin

Pull-Request: #1706
Reviewed-by: Jean Privat <jean@pryen.org>
Reviewed-by: Alexandre Blondin Massé <alexandre.blondin.masse@gmail.com>

diff --git a/lib/graphs/digraph.nit b/lib/graphs/digraph.nit
index 8f45495..bc9a8af 100644 (file)
--- a/lib/graphs/digraph.nit
+++ b/lib/graphs/digraph.nit
@@ -117,7 +117,7 @@
 # g.add_arcs([[1,2],[2,1],[2,3],[3,4],[4,5],[5,3]])
 # for component in g.strongly_connected_components.to_partitions
 # do
-#      print component
+#      print component
 # end
 # # Prints [1,2] and [3,4,5]
 # ~~~
@@ -291,7 +291,7 @@ interface Digraph[V: Object]
        # g.add_arc(0, 2)
        # g.add_arc(1, 2)
        # for arc in g.arcs_iterator do
-       #       assert g.has_arc(arc[0], arc[1])
+       #       assert g.has_arc(arc[0], arc[1])
        # end
        # ~~~
        fun arcs_iterator: Iterator[Array[V]] do return new ArcsIterator[V](self)
@@ -317,7 +317,7 @@ interface Digraph[V: Object]
        # g.add_arc(1, 3)
        # g.add_arc(2, 3)
        # for arc in g.incoming_arcs(3) do
-       #       assert g.is_predecessor(arc[0], arc[1])
+       #       assert g.is_predecessor(arc[0], arc[1])
        # end
        # ~~~
        fun incoming_arcs(u: V): Collection[Array[V]]
@@ -340,7 +340,7 @@ interface Digraph[V: Object]
        # g.add_arc(2, 3)
        # g.add_arc(1, 2)
        # for arc in g.outgoing_arcs(1) do
-       #       assert g.is_successor(arc[1], arc[0])
+       #       assert g.is_successor(arc[1], arc[0])
        # end
        # ~~~
        fun outgoing_arcs(u: V): Collection[Array[V]]
@@ -383,6 +383,15 @@ interface Digraph[V: Object]
                return s
        end
 
+       # Open Graphviz with `self.to_dot`.
+       #
+       # Mainly used for debugging.
+       fun show_dot do
+               var f = new ProcessWriter("dot", "-Txlib")
+               f.write to_dot
+               f.close
+       end
+
        ## ------------ ##
        ## Neighborhood ##
        ## ------------ ##

diff --git a/lib/graphs/pagerank.nit b/lib/graphs/pagerank.nit
new file mode 100644 (file)
index 0000000..5177e5a
--- /dev/null
+++ b/lib/graphs/pagerank.nit
@@ -0,0 +1,88 @@
+# This file is part of NIT (http://www.nitlanguage.org).
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# Add PageRank computation for vertices in Digraph.
+module pagerank
+
+import graphs::digraph
+
+redef class Digraph[V]
+
+       # Compute PageRank for each vertex
+       #
+       # Details of the algorithm can be found in:
+       # > L. Page, S. Brin, R. Motwani, and T.Winograd.
+       # > **The pagerank citation ranking: Bringing order to the web.**
+       # > *Technical report, Stanford Digital Library Technologies Project, 1998*
+       #
+       # Example:
+       # ~~~
+       # var g = new HashDigraph[String]
+       # g.add_arc("A", "B")
+       # g.add_arc("A", "C")
+       # g.add_arc("B", "C")
+       # g.add_arc("C", "A")
+       # g.add_arc("D", "C")
+       #
+       # assert g.pagerank.join(", ", ":") == "A:1.488, B:0.782, C:1.575, D:0.15"
+       # ~~~
+       fun pagerank: PRMap[V] do
+               # `d` constant such as `initial_pagerank(node) == (1 - d) != 0`
+               var d = 0.85 # commonly-choosen value
+               # Init each node page rank with an initial_value
+               var values = new PRMap[V]
+               var vertices = self.vertices
+               for v in vertices do values[v] = 1.0 - d
+               # Compute page rank until convergence
+               var prev = new PRMap[V]
+               while not values.is_approx(prev, 0.001) do
+                       prev = new PRMap[V].from(values)
+                       for v in vertices do
+                               var in_pr = 0.0
+                               for o in predecessors(v) do
+                                       in_pr += values[o] / out_degree(o).to_f
+                               end
+                               values[v] = (1.0 - d) + d * in_pr
+                       end
+               end
+               return values
+       end
+end
+
+# Map each Vertice of a Digraph to it's PageRank.
+#
+# See: `Digraph::pagerank`.
+class PRMap[V]
+       super HashMap[V, Float]
+
+       # Init `self` by copying `other` values.
+       init from(other: PRMap[V]) do
+               init
+               for k, v in other do self[k] = v
+       end
+
+       # Is `self` approximately equal to another PRMap?
+       #
+       # `self` is approximately equal to `o` if `o` contains all the key from `self`
+       # with the same values.
+       #
+       # Values equality is based on `Float::is_approx` with `precision`.
+       fun is_approx(o: SELF, precision: Float): Bool do
+               for k1, v1 in self do
+                       if not o.has_key(k1) then return false
+                       if not v1.is_approx(o[k1], precision) then return false
+               end
+               return true
+       end
+end