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graph/graphs/gen: make NavigableSmallWorld use dst's edge and node constructors

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This changes the behaviour of the function to create the small world graph as
a disconnected subgraph in g rather than applying the algorithm to potentially
already existing nodes in g.
This commit is contained in:
Dan Kortschak
2018-10-21 18:13:39 +10:30
committed by Dan Kortschak
parent 75ba0793c2
commit f021a2e7da
2 changed files with 36 additions and 32 deletions
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63
graph/graphs/gen/small_world.go
View File

@@ -12,16 +12,15 @@ import (
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/graph"
"gonum.org/v1/gonum/graph/simple"
"gonum.org/v1/gonum/stat/sampleuv"
)
// NavigableSmallWorld constructs an N-dimensional grid with guaranteed local connectivity
// and random long-range connectivity in the destination, dst. The dims parameters specifies
// the length of each of the N dimensions, p defines the Manhattan distance between local
// nodes, and q defines the number of out-going long-range connections from each node. Long-
// range connections are made with a probability proportional to |d(u,v)|^-r where d is the
// Manhattan distance between non-local nodes.
// and random long-range connectivity as a subgraph in the destination, dst.
// The dims parameters specifies the length of each of the N dimensions, p defines the
// Manhattan distance between local nodes, and q defines the number of out-going long-range
// connections from each node. Long-range connections are made with a probability
// proportional to |d(u,v)|^-r where d is the Manhattan distance between non-local nodes.
//
// The algorithm is essentially as described on p4 of http://www.cs.cornell.edu/home/kleinber/swn.pdf.
func NavigableSmallWorld(dst GraphBuilder, dims []int, p, q int, r float64, src rand.Source) (err error) {
@@ -39,10 +38,11 @@ func NavigableSmallWorld(dst GraphBuilder, dims []int, p, q int, r float64, src
for _, d := range dims {
n *= d
}
for i := 0; i < n; i++ {
if dst.Node(int64(i)) == nil {
dst.AddNode(simple.Node(i))
}
nodes := make([]graph.Node, n)
for i := range nodes {
u := dst.NewNode()
dst.AddNode(u)
nodes[i] = u
}
hasEdge := dst.HasEdgeBetween
@@ -56,26 +56,25 @@ func NavigableSmallWorld(dst GraphBuilder, dims []int, p, q int, r float64, src
locality[i] = p*2 + 1
}
iterateOver(dims, func(u []int) {
uid := idFrom(u, dims)
un := nodes[idxFrom(u, dims)]
iterateOver(locality, func(delta []int) {
d := manhattanDelta(u, delta, dims, -p)
if d == 0 || d > p {
return
}
vid := idFromDelta(u, delta, dims, -p)
e := simple.Edge{F: simple.Node(uid), T: simple.Node(vid)}
if uid > vid {
e.F, e.T = e.T, e.F
vn := nodes[idxFromDelta(u, delta, dims, -p)]
if un.ID() > vn.ID() {
un, vn = vn, un
}
if !hasEdge(e.From().ID(), e.To().ID()) {
dst.SetEdge(e)
if !hasEdge(un.ID(), vn.ID()) {
dst.SetEdge(dst.NewEdge(un, vn))
}
if !isDirected {
return
}
e.F, e.T = e.T, e.F
if !hasEdge(e.From().ID(), e.To().ID()) {
dst.SetEdge(e)
un, vn = vn, un
if !hasEdge(un.ID(), vn.ID()) {
dst.SetEdge(dst.NewEdge(un, vn))
}
})
})
@@ -92,26 +91,26 @@ func NavigableSmallWorld(dst GraphBuilder, dims []int, p, q int, r float64, src
w := make([]float64, n)
ws := sampleuv.NewWeighted(w, src)
iterateOver(dims, func(u []int) {
uid := idFrom(u, dims)
un := nodes[idxFrom(u, dims)]
iterateOver(dims, func(v []int) {
d := manhattanBetween(u, v)
if d <= p {
return
}
w[idFrom(v, dims)] = math.Pow(float64(d), -r)
w[idxFrom(v, dims)] = math.Pow(float64(d), -r)
})
ws.ReweightAll(w)
for i := 0; i < q; i++ {
vid, ok := ws.Take()
vidx, ok := ws.Take()
if !ok {
panic("depleted distribution")
}
e := simple.Edge{F: simple.Node(uid), T: simple.Node(vid)}
if !isDirected && uid > vid {
e.F, e.T = e.T, e.F
vn := nodes[vidx]
if !isDirected && un.ID() > vn.ID() {
un, vn = vn, un
}
if !hasEdge(e.From().ID(), e.To().ID()) {
dst.SetEdge(e)
if !hasEdge(un.ID(), vn.ID()) {
dst.SetEdge(dst.NewEdge(un, vn))
}
}
for i := range w {
@@ -173,8 +172,8 @@ func manhattanDelta(a, delta, dims []int, translate int) int {
return d
}
// idFrom returns a node id for the slice n over the given dimensions.
func idFrom(n, dims []int) int {
// idxFrom returns a node index for the slice n over the given dimensions.
func idxFrom(n, dims []int) int {
s := 1
var id int
for d, m := range dims {
@@ -188,9 +187,9 @@ func idFrom(n, dims []int) int {
return id
}
// idFromDelta returns a node id for the slice base plus the delta over the given
// idxFromDelta returns a node index for the slice base plus the delta over the given
// dimensions and applying the translation.
func idFromDelta(base, delta, dims []int, translate int) int {
func idxFromDelta(base, delta, dims []int, translate int) int {
s := 1
var id int
for d, m := range dims {

5
graph/graphs/gen/small_world_test.go
View File

@@ -22,6 +22,8 @@ func TestNavigableSmallWorldUndirected(t *testing.T) {
for r := 0.5; r < 10; r++ {
for _, dims := range smallWorldDimensionParameters {
g := &gnUndirected{UndirectedBuilder: simple.NewUndirectedGraph()}
orig := g.NewNode()
g.AddNode(orig)
err := NavigableSmallWorld(g, dims, p, q, r, nil)
n := 1
for _, d := range dims {
@@ -30,6 +32,9 @@ func TestNavigableSmallWorldUndirected(t *testing.T) {
if err != nil {
t.Fatalf("unexpected error: dims=%v n=%d, p=%d, q=%d, r=%v: %v", dims, n, p, q, r, err)
}
if g.From(orig.ID()).Len() != 0 {
t.Errorf("edge added from already existing node: dims=%v n=%d, p=%d, q=%d, r=%v", dims, n, p, q, r)
}
if g.addBackwards {
t.Errorf("edge added with From.ID > To.ID: dims=%v n=%d, p=%d, q=%d, r=%v", dims, n, p, q, r)
}