Faster dorogovtsev mendes (#371)

* Optimized dorogovtsev_mendes implementation

* format

* Fixed index

* Added a Test

* Update src/SimpleGraphs/generators/randgraphs.jl

As suggested

Co-authored-by: Guillaume Dalle <[email protected]>

* Update src/SimpleGraphs/generators/randgraphs.jl

---------

Co-authored-by: Guillaume Dalle <[email protected]>

Author: AntoineBut

src/SimpleGraphs/generators/randgraphs.jl

@@ -1494,24 +1494,28 @@ function dorogovtsev_mendes(
     n < 3 && throw(DomainError("n=$n must be at least 3"))
     rng = rng_from_rng_or_seed(rng, seed)
     g = cycle_graph(3)
+    bag_of_edges = Vector{SimpleEdge{Int}}(undef, 2 * n - 3) # Caching edges as they are added to avoid costly lookups
 
-    for iteration in 1:(n - 3)
-        chosenedge = rand(rng, 1:(2 * ne(g))) # undirected so each edge is listed twice in adjlist
-        u, v = -1, -1
-        for i in 1:nv(g)
-            edgelist = outneighbors(g, i)
-            if chosenedge > length(edgelist)
-                chosenedge -= length(edgelist)
-            else
-                u = i
-                v = edgelist[chosenedge]
-                break
-            end
-        end
+    bag_of_edges[1] = SimpleEdge(1, 2)
+    bag_of_edges[2] = SimpleEdge(1, 3)
+    bag_of_edges[3] = SimpleEdge(2, 3)
+    index = 3
 
+    for _ in 1:(n - 3)
+        # Choose random edge from bag
+        edge = bag_of_edges[rand(rng, 1:index)]
+        u, v = src(edge), dst(edge)
+
+        # Add new vertex
         add_vertex!(g)
+        # Add new edges
         add_edge!(g, nv(g), u)
         add_edge!(g, nv(g), v)
+
+        # Add new edges to bag
+        bag_of_edges[index + 1] = SimpleEdge(nv(g), edge.src)
+        bag_of_edges[index + 2] = SimpleEdge(nv(g), edge.dst)
+        index += 2
     end
     return g
 end

test/simplegraphs/generators/randgraphs.jl

@@ -382,6 +382,19 @@
         @test δ(g) == 2
         g = dorogovtsev_mendes(3; rng=rng)
         @test nv(g) == 3 && ne(g) == 3
+        @test δ(g) == 2 && Δ(g) == 2
+
+        # Testing that n=4 graph is one on the possible graphs
+        g = dorogovtsev_mendes(4; rng=rng)
+        @test has_edge(g, 1, 2) &&
+            has_edge(g, 1, 3) &&
+            has_edge(g, 2, 3) &&
+            (
+                has_edge(g, 1, 4) && has_edge(g, 2, 4) ||
+                has_edge(g, 2, 4) && has_edge(g, 3, 4) ||
+                has_edge(g, 1, 4) && has_edge(g, 3, 4)
+            )
+
         # testing domain errors
         @test_throws DomainError dorogovtsev_mendes(2, rng=rng)
         @test_throws DomainError dorogovtsev_mendes(-1, rng=rng)