// Kruskal generates a minimum spanning tree of g by greedy tree coalescence, placing
// the result in the destination, dst. If the edge weights of g are distinct
// it will be the unique minimum spanning tree of g. The destination is not cleared
// first. The weight of the minimum spanning tree is returned. If g is not connected,
// a minimum spanning forest will be constructed in dst and the sum of minimum
// spanning tree weights will be returned.
func Kruskal(dst graph.UndirectedBuilder, g UndirectedWeightLister) float64 {
edges := g.Edges()
ascend := make([]simple.Edge, 0, len(edges))
for _, e := range edges {
u := e.From()
v := e.To()
w, ok := g.Weight(u, v)
if !ok {
panic("kruskal: unexpected invalid weight")
}
ascend = append(ascend, simple.Edge{F: u, T: v, W: w})
}
sort.Sort(byWeight(ascend))
ds := newDisjointSet()
for _, node := range g.Nodes() {
ds.makeSet(node.ID())
}
var w float64
for _, e := range ascend {
if s1, s2 := ds.find(e.From().ID()), ds.find(e.To().ID()); s1 != s2 {
ds.union(s1, s2)
dst.SetEdge(e)
w += e.Weight()
}
}
return w
}
// Prim generates a minimum spanning tree of g by greedy tree extension, placing
// the result in the destination, dst. If the edge weights of g are distinct
// it will be the unique minimum spanning tree of g. The destination is not cleared
// first. The weight of the minimum spanning tree is returned. If g is not connected,
// a minimum spanning forest will be constructed in dst and the sum of minimum
// spanning tree weights will be returned.
func Prim(dst graph.UndirectedBuilder, g UndirectedWeighter) float64 {
nodes := g.Nodes()
if len(nodes) == 0 {
return 0
}
q := &primQueue{
indexOf: make(map[int]int, len(nodes)-1),
nodes: make([]simple.Edge, 0, len(nodes)-1),
}
for _, u := range nodes[1:] {
heap.Push(q, simple.Edge{F: u, W: math.Inf(1)})
}
u := nodes[0]
for _, v := range g.From(u) {
w, ok := g.Weight(u, v)
if !ok {
panic("prim: unexpected invalid weight")
}
q.update(v, u, w)
}
var w float64
for q.Len() > 0 {
e := heap.Pop(q).(simple.Edge)
if e.To() != nil && g.HasEdgeBetween(e.From(), e.To()) {
dst.SetEdge(e)
w += e.Weight()
}
u = e.From()
for _, n := range g.From(u) {
if key, ok := q.key(n); ok {
w, ok := g.Weight(u, n)
if !ok {
panic("prim: unexpected invalid weight")
}
if w < key {
q.update(n, u, w)
}
}
}
}
return w
}
// PreferentialAttachment constructs a graph in the destination, dst, of order n.
// The graph is constructed successively starting from an m order graph with one
// node having degree m-1. At each iteration of graph addition, one node is added
// with m additional edges joining existing nodes with probability proportional
// to the nodes' degrees. If src is not nil it is used as the random source,
// otherwise rand.Float64 is used.
//
// The algorithm is essentially as described in http://arxiv.org/abs/cond-mat/0110452
// after 10.1126/science.286.5439.509.
func PreferentialAttachment(dst graph.UndirectedBuilder, n, m int, src *rand.Rand) error {
if n <= m {
return fmt.Errorf("gen: n <= m: n=%v m=%d", n, m)
}
// Initial condition.
wt := make([]float64, n)
for u := 0; u < m; u++ {
if !dst.Has(simple.Node(u)) {
dst.AddNode(simple.Node(u))
}
// We need to give equal probability for
// adding the first generation of edges.
wt[u] = 1
}
ws := sample.NewWeighted(wt, src)
for i := range wt {
// These weights will organically grow
// after the first growth iteration.
wt[i] = 0
}
// Growth.
for v := m; v < n; v++ {
for i := 0; i < m; i++ {
// Preferential attachment.
u, ok := ws.Take()
if !ok {
return errors.New("gen: depleted distribution")
}
dst.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
wt[u]++
wt[v]++
}
ws.ReweightAll(wt)
}
return nil
}
// TunableClusteringScaleFree constructs a graph in the destination, dst, of order n.
// The graph is constructed successively starting from an m order graph with one node
// having degree m-1. At each iteration of graph addition, one node is added with m
// additional edges joining existing nodes with probability proportional to the nodes'
// degrees. The edges are formed as a triad with probability, p.
// If src is not nil it is used as the random source, otherwise rand.Float64 and
// rand.Intn are used.
//
// The algorithm is essentially as described in http://arxiv.org/abs/cond-mat/0110452.
func TunableClusteringScaleFree(dst graph.UndirectedBuilder, n, m int, p float64, src *rand.Rand) error {
if p < 0 || p > 1 {
return fmt.Errorf("gen: bad probability: p=%v", p)
}
if n <= m {
return fmt.Errorf("gen: n <= m: n=%v m=%d", n, m)
}
var (
rnd func() float64
rndN func(int) int
)
if src == nil {
rnd = rand.Float64
rndN = rand.Intn
} else {
rnd = src.Float64
rndN = src.Intn
}
// Initial condition.
wt := make([]float64, n)
for u := 0; u < m; u++ {
if !dst.Has(simple.Node(u)) {
dst.AddNode(simple.Node(u))
}
// We need to give equal probability for
// adding the first generation of edges.
wt[u] = 1
}
ws := sample.NewWeighted(wt, src)
for i := range wt {
// These weights will organically grow
// after the first growth iteration.
wt[i] = 0
}
// Growth.
for v := m; v < n; v++ {
var u int
pa:
for i := 0; i < m; i++ {
// Triad formation.
if i != 0 && rnd() < p {
for _, w := range permute(dst.From(simple.Node(u)), rndN) {
wid := w.ID()
if wid == v || dst.HasEdgeBetween(w, simple.Node(v)) {
continue
}
dst.SetEdge(simple.Edge{F: w, T: simple.Node(v), W: 1})
wt[wid]++
wt[v]++
continue pa
}
}
// Preferential attachment.
for {
var ok bool
u, ok = ws.Take()
if !ok {
return errors.New("gen: depleted distribution")
}
if u == v || dst.HasEdgeBetween(simple.Node(u), simple.Node(v)) {
continue
}
dst.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v), W: 1})
wt[u]++
wt[v]++
break
}
}
ws.ReweightAll(wt)
}
return nil
}
