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Diffstat (limited to 'vendor/github.com/soniakeys/graph/random.go')
| -rw-r--r-- | vendor/github.com/soniakeys/graph/random.go | 325 |
1 files changed, 325 insertions, 0 deletions
diff --git a/vendor/github.com/soniakeys/graph/random.go b/vendor/github.com/soniakeys/graph/random.go new file mode 100644 index 0000000..99f0445 --- /dev/null +++ b/vendor/github.com/soniakeys/graph/random.go @@ -0,0 +1,325 @@ +// Copyright 2016 Sonia Keys +// License MIT: https://opensource.org/licenses/MIT + +package graph + +import ( + "errors" + "math" + "math/rand" + "time" +) + +// Euclidean generates a random simple graph on the Euclidean plane. +// +// Nodes are associated with coordinates uniformly distributed on a unit +// square. Arcs are added between random nodes with a bias toward connecting +// nearer nodes. +// +// Unfortunately the function has a few "knobs". +// The returned graph will have order nNodes and arc size nArcs. The affinity +// argument controls the bias toward connecting nearer nodes. The function +// selects random pairs of nodes as a candidate arc then rejects the candidate +// if the nodes fail an affinity test. Also parallel arcs are rejected. +// As more affine or denser graphs are requested, rejections increase, +// increasing run time. The patience argument controls the number of arc +// rejections allowed before the function gives up and returns an error. +// Note that higher affinity will require more patience and that some +// combinations of nNodes and nArcs cannot be achieved with any amount of +// patience given that the returned graph must be simple. +// +// If Rand r is nil, the method creates a new source and generator for +// one-time use. +// +// Returned is a directed simple graph and associated positions indexed by +// node number. +// +// See also LabeledEuclidean. +func Euclidean(nNodes, nArcs int, affinity float64, patience int, r *rand.Rand) (g Directed, pos []struct{ X, Y float64 }, err error) { + a := make(AdjacencyList, nNodes) // graph + // generate random positions + if r == nil { + r = rand.New(rand.NewSource(time.Now().UnixNano())) + } + pos = make([]struct{ X, Y float64 }, nNodes) + for i := range pos { + pos[i].X = r.Float64() + pos[i].Y = r.Float64() + } + // arcs + var tooFar, dup int +arc: + for i := 0; i < nArcs; { + if tooFar == nArcs*patience { + err = errors.New("affinity not found") + return + } + if dup == nArcs*patience { + err = errors.New("overcrowding") + return + } + n1 := NI(r.Intn(nNodes)) + var n2 NI + for { + n2 = NI(r.Intn(nNodes)) + if n2 != n1 { // no graph loops + break + } + } + c1 := &pos[n1] + c2 := &pos[n2] + dist := math.Hypot(c2.X-c1.X, c2.Y-c1.Y) + if dist*affinity > r.ExpFloat64() { // favor near nodes + tooFar++ + continue + } + for _, nb := range a[n1] { + if nb == n2 { // no parallel arcs + dup++ + continue arc + } + } + a[n1] = append(a[n1], n2) + i++ + } + g = Directed{a} + return +} + +// LabeledEuclidean generates a random simple graph on the Euclidean plane. +// +// Arc label values in the returned graph g are indexes into the return value +// wt. Wt is the Euclidean distance between the from and to nodes of the arc. +// +// Otherwise the function arguments and return values are the same as for +// function Euclidean. See Euclidean. +func LabeledEuclidean(nNodes, nArcs int, affinity float64, patience int, r *rand.Rand) (g LabeledDirected, pos []struct{ X, Y float64 }, wt []float64, err error) { + a := make(LabeledAdjacencyList, nNodes) // graph + wt = make([]float64, nArcs) // arc weights + // generate random positions + if r == nil { + r = rand.New(rand.NewSource(time.Now().UnixNano())) + } + pos = make([]struct{ X, Y float64 }, nNodes) + for i := range pos { + pos[i].X = r.Float64() + pos[i].Y = r.Float64() + } + // arcs + var tooFar, dup int +arc: + for i := 0; i < nArcs; { + if tooFar == nArcs*patience { + err = errors.New("affinity not found") + return + } + if dup == nArcs*patience { + err = errors.New("overcrowding") + return + } + n1 := NI(r.Intn(nNodes)) + var n2 NI + for { + n2 = NI(r.Intn(nNodes)) + if n2 != n1 { // no graph loops + break + } + } + c1 := &pos[n1] + c2 := &pos[n2] + dist := math.Hypot(c2.X-c1.X, c2.Y-c1.Y) + if dist*affinity > r.ExpFloat64() { // favor near nodes + tooFar++ + continue + } + for _, nb := range a[n1] { + if nb.To == n2 { // no parallel arcs + dup++ + continue arc + } + } + wt[i] = dist + a[n1] = append(a[n1], Half{n2, LI(i)}) + i++ + } + g = LabeledDirected{a} + return +} + +// Geometric generates a random geometric graph (RGG) on the Euclidean plane. +// +// An RGG is an undirected simple graph. Nodes are associated with coordinates +// uniformly distributed on a unit square. Edges are added between all nodes +// falling within a specified distance or radius of each other. +// +// The resulting number of edges is somewhat random but asymptotically +// approaches m = πr²n²/2. The method accumulates and returns the actual +// number of edges constructed. +// +// If Rand r is nil, the method creates a new source and generator for +// one-time use. +// +// See also LabeledGeometric. +func Geometric(nNodes int, radius float64, r *rand.Rand) (g Undirected, pos []struct{ X, Y float64 }, m int) { + // Expected degree is approximately nπr². + a := make(AdjacencyList, nNodes) + if r == nil { + r = rand.New(rand.NewSource(time.Now().UnixNano())) + } + pos = make([]struct{ X, Y float64 }, nNodes) + for i := range pos { + pos[i].X = r.Float64() + pos[i].Y = r.Float64() + } + for u, up := range pos { + for v := u + 1; v < len(pos); v++ { + vp := pos[v] + if math.Hypot(up.X-vp.X, up.Y-vp.Y) < radius { + a[u] = append(a[u], NI(v)) + a[v] = append(a[v], NI(u)) + m++ + } + } + } + g = Undirected{a} + return +} + +// LabeledGeometric generates a random geometric graph (RGG) on the Euclidean +// plane. +// +// Edge label values in the returned graph g are indexes into the return value +// wt. Wt is the Euclidean distance between nodes of the edge. The graph +// size m is len(wt). +// +// See Geometric for additional description. +func LabeledGeometric(nNodes int, radius float64, r *rand.Rand) (g LabeledUndirected, pos []struct{ X, Y float64 }, wt []float64) { + a := make(LabeledAdjacencyList, nNodes) + if r == nil { + r = rand.New(rand.NewSource(time.Now().UnixNano())) + } + pos = make([]struct{ X, Y float64 }, nNodes) + for i := range pos { + pos[i].X = r.Float64() + pos[i].Y = r.Float64() + } + for u, up := range pos { + for v := u + 1; v < len(pos); v++ { + vp := pos[v] + if w := math.Hypot(up.X-vp.X, up.Y-vp.Y); w < radius { + a[u] = append(a[u], Half{NI(v), LI(len(wt))}) + a[v] = append(a[v], Half{NI(u), LI(len(wt))}) + wt = append(wt, w) + } + } + } + g = LabeledUndirected{a} + return +} + +// KroneckerDirected generates a Kronecker-like random directed graph. +// +// The returned graph g is simple and has no isolated nodes but is not +// necessarily fully connected. The number of of nodes will be <= 2^scale, +// and will be near 2^scale for typical values of arcFactor, >= 2. +// ArcFactor * 2^scale arcs are generated, although loops and duplicate arcs +// are rejected. +// +// If Rand r is nil, the method creates a new source and generator for +// one-time use. +// +// Return value ma is the number of arcs retained in the result graph. +func KroneckerDirected(scale uint, arcFactor float64, r *rand.Rand) (g Directed, ma int) { + a, m := kronecker(scale, arcFactor, true, r) + return Directed{a}, m +} + +// KroneckerUndirected generates a Kronecker-like random undirected graph. +// +// The returned graph g is simple and has no isolated nodes but is not +// necessarily fully connected. The number of of nodes will be <= 2^scale, +// and will be near 2^scale for typical values of edgeFactor, >= 2. +// EdgeFactor * 2^scale edges are generated, although loops and duplicate edges +// are rejected. +// +// If Rand r is nil, the method creates a new source and generator for +// one-time use. +// +// Return value m is the true number of edges--not arcs--retained in the result +// graph. +func KroneckerUndirected(scale uint, edgeFactor float64, r *rand.Rand) (g Undirected, m int) { + al, s := kronecker(scale, edgeFactor, false, r) + return Undirected{al}, s +} + +// Styled after the Graph500 example code. Not well tested currently. +// Graph500 example generates undirected only. No idea if the directed variant +// here is meaningful or not. +// +// note mma returns arc size ma for dir=true, but returns size m for dir=false +func kronecker(scale uint, edgeFactor float64, dir bool, r *rand.Rand) (g AdjacencyList, mma int) { + if r == nil { + r = rand.New(rand.NewSource(time.Now().UnixNano())) + } + N := NI(1 << scale) // node extent + M := int(edgeFactor*float64(N) + .5) // number of arcs/edges to generate + a, b, c := 0.57, 0.19, 0.19 // initiator probabilities + ab := a + b + cNorm := c / (1 - ab) + aNorm := a / ab + ij := make([][2]NI, M) + var bm Bits + var nNodes int + for k := range ij { + var i, j NI + for b := NI(1); b < N; b <<= 1 { + if r.Float64() > ab { + i |= b + if r.Float64() > cNorm { + j |= b + } + } else if r.Float64() > aNorm { + j |= b + } + } + if bm.Bit(i) == 0 { + bm.SetBit(i, 1) + nNodes++ + } + if bm.Bit(j) == 0 { + bm.SetBit(j, 1) + nNodes++ + } + r := r.Intn(k + 1) // shuffle edges as they are generated + ij[k] = ij[r] + ij[r] = [2]NI{i, j} + } + p := r.Perm(nNodes) // mapping to shuffle IDs of non-isolated nodes + px := 0 + rn := make([]NI, N) + for i := range rn { + if bm.Bit(NI(i)) == 1 { + rn[i] = NI(p[px]) // fill lookup table + px++ + } + } + g = make(AdjacencyList, nNodes) +ij: + for _, e := range ij { + if e[0] == e[1] { + continue // skip loops + } + ri, rj := rn[e[0]], rn[e[1]] + for _, nb := range g[ri] { + if nb == rj { + continue ij // skip parallel edges + } + } + g[ri] = append(g[ri], rj) + mma++ + if !dir { + g[rj] = append(g[rj], ri) + } + } + return +} |
