예제 #1
0
// 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
}
예제 #2
0
// 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
}
예제 #3
0
// 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
}
예제 #4
0
// 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
}