Reduce the time-complexity of the network initial positioning. (#2759)

* Reduce the time-complexity of the network initial positioning. Very substantial performance gain for large graphs.

* Remove unwanted console messages, extended comment.

lib/network/modules/KamadaKawai.js

@@ -49,11 +49,14 @@ class KamadaKawai {
     // get the K Matrix
     this._createK_matrix(D_matrix);
 
+    // initial E Matrix
+    this._createE_matrix();
+
     // calculate positions
     let threshold = 0.01;
     let innerThreshold = 1;
     let iterations = 0;
-    let maxIterations = Math.max(1000,Math.min(10*this.body.nodeIndices.length,6000));
+    let maxIterations = Math.max(1000, Math.min(10 * this.body.nodeIndices.length, 6000));
     let maxInnerIterations = 5;
 
     let maxEnergy = 1e9;
@@ -64,10 +67,10 @@ class KamadaKawai {
       [highE_nodeId, maxEnergy, dE_dx, dE_dy] = this._getHighestEnergyNode(ignoreClusters);
       delta_m = maxEnergy;
       subIterations = 0;
-      while(delta_m > innerThreshold && subIterations < maxInnerIterations) {
+      while (delta_m > innerThreshold && subIterations < maxInnerIterations) {
         subIterations += 1;
         this._moveNode(highE_nodeId, dE_dx, dE_dy);
-        [delta_m,dE_dx,dE_dy] = this._getEnergy(highE_nodeId);
+        [delta_m, dE_dx, dE_dy] = this._getEnergy(highE_nodeId);
       }
     }
   }
@@ -87,7 +90,7 @@ class KamadaKawai {
     for (let nodeIdx = 0; nodeIdx < nodesArray.length; nodeIdx++) {
       let m = nodesArray[nodeIdx];
       // by not evaluating nodes with predefined positions we should only move nodes that have no positions.
-      if ((nodes[m].predefinedPosition === false || nodes[m].isCluster === true && ignoreClusters === true) || nodes[m].options.fixed.x === true ||  nodes[m].options.fixed.y === true) {
+      if ((nodes[m].predefinedPosition === false || nodes[m].isCluster === true && ignoreClusters === true) || nodes[m].options.fixed.x === true || nodes[m].options.fixed.y === true) {
         let [delta_m,dE_dx,dE_dy] = this._getEnergy(m);
         if (maxEnergy < delta_m) {
           maxEnergy = delta_m;
@@ -108,24 +111,7 @@ class KamadaKawai {
    * @private
    */
   _getEnergy(m) {
-    let nodesArray = this.body.nodeIndices;
-    let nodes = this.body.nodes;
-
-    let x_m = nodes[m].x;
-    let y_m = nodes[m].y;
-    let dE_dx = 0;
-    let dE_dy = 0;
-    for (let iIdx = 0; iIdx < nodesArray.length; iIdx++) {
-      let i = nodesArray[iIdx];
-      if (i !== m) {
-        let x_i = nodes[i].x;
-        let y_i = nodes[i].y;
-        let denominator = 1.0 / Math.sqrt(Math.pow(x_m - x_i, 2) + Math.pow(y_m - y_i, 2));
-        dE_dx += this.K_matrix[m][i] * ((x_m - x_i) - this.L_matrix[m][i] * (x_m - x_i) * denominator);
-        dE_dy += this.K_matrix[m][i] * ((y_m - y_i) - this.L_matrix[m][i] * (y_m - y_i) * denominator);
-      }
-    }
-
+    let [dE_dx,dE_dy] = this.E_sums[m];
     let delta_m = Math.sqrt(Math.pow(dE_dx, 2) + Math.pow(dE_dy, 2));
     return [delta_m, dE_dx, dE_dy];
   }
@@ -147,15 +133,20 @@ class KamadaKawai {
 
     let x_m = nodes[m].x;
     let y_m = nodes[m].y;
+    let km = this.K_matrix[m];
+    let lm = this.L_matrix[m];
+
     for (let iIdx = 0; iIdx < nodesArray.length; iIdx++) {
       let i = nodesArray[iIdx];
       if (i !== m) {
         let x_i = nodes[i].x;
         let y_i = nodes[i].y;
+        let kmat = km[i];
+        let lmat = lm[i];
         let denominator = 1.0 / Math.pow(Math.pow(x_m - x_i, 2) + Math.pow(y_m - y_i, 2), 1.5);
-        d2E_dx2 += this.K_matrix[m][i] * (1 - this.L_matrix[m][i] * Math.pow(y_m - y_i, 2) * denominator);
-        d2E_dxdy += this.K_matrix[m][i] * (this.L_matrix[m][i] * (x_m - x_i) * (y_m - y_i) * denominator);
-        d2E_dy2 += this.K_matrix[m][i] * (1 - this.L_matrix[m][i] * Math.pow(x_m - x_i, 2) * denominator);
+        d2E_dx2 += kmat * (1 - lmat * Math.pow(y_m - y_i, 2) * denominator);
+        d2E_dxdy += kmat * (lmat * (x_m - x_i) * (y_m - y_i) * denominator);
+        d2E_dy2 += kmat * (1 - lmat * Math.pow(x_m - x_i, 2) * denominator);
       }
     }
     // make the variable names easier to make the solving of the linear system easier to read
@@ -168,6 +159,9 @@ class KamadaKawai {
     // move the node
     nodes[m].x += dx;
     nodes[m].y += dy;
+
+    // Recalculate E_matrix (should be incremental)
+    this._updateE_matrix(m);
   }
 
 
@@ -208,8 +202,82 @@ class KamadaKawai {
     }
   }
 
+  /**
+   *  Create matrix with all energies between nodes
+   *  @private
+   */
+  _createE_matrix() {
+    let nodesArray = this.body.nodeIndices;
+    let nodes = this.body.nodes;
+    this.E_matrix = {};
+    this.E_sums = {};
+    for (let mIdx = 0; mIdx < nodesArray.length; mIdx++) {
+      this.E_matrix[nodesArray[mIdx]] = [];
+    }
+    for (let mIdx = 0; mIdx < nodesArray.length; mIdx++) {
+      let m = nodesArray[mIdx];
+      let x_m = nodes[m].x;
+      let y_m = nodes[m].y;
+      let dE_dx = 0;
+      let dE_dy = 0;
+      for (let iIdx = mIdx; iIdx < nodesArray.length; iIdx++) {
+        let i = nodesArray[iIdx];
+        if (i !== m) {
+          let x_i = nodes[i].x;
+          let y_i = nodes[i].y;
+          let denominator = 1.0 / Math.sqrt(Math.pow(x_m - x_i, 2) + Math.pow(y_m - y_i, 2));
+          this.E_matrix[m][iIdx] = [
+            this.K_matrix[m][i] * ((x_m - x_i) - this.L_matrix[m][i] * (x_m - x_i) * denominator),
+            this.K_matrix[m][i] * ((y_m - y_i) - this.L_matrix[m][i] * (y_m - y_i) * denominator)
+          ];
+          this.E_matrix[i][mIdx] = this.E_matrix[m][iIdx];
+          dE_dx += this.E_matrix[m][iIdx][0];
+          dE_dy += this.E_matrix[m][iIdx][1];
+        }
+      }
+      //Store sum
+      this.E_sums[m] = [dE_dx, dE_dy];
+    }
+  }
+
+  //Update method, just doing single column (rows are auto-updated) (update all sums)
+  _updateE_matrix(m) {
+    let nodesArray = this.body.nodeIndices;
+    let nodes = this.body.nodes;
+    let colm = this.E_matrix[m];
+    let kcolm = this.K_matrix[m];
+    let lcolm = this.L_matrix[m];
+    let x_m = nodes[m].x;
+    let y_m = nodes[m].y;
+    let dE_dx = 0;
+    let dE_dy = 0;
+    for (let iIdx = 0; iIdx < nodesArray.length; iIdx++) {
+      let i = nodesArray[iIdx];
+      if (i !== m) {
+        //Keep old energy value for sum modification below
+        let cell = colm[iIdx];
+        let oldDx = cell[0];
+        let oldDy = cell[1];
 
+        //Calc new energy:
+        let x_i = nodes[i].x;
+        let y_i = nodes[i].y;
+        let denominator = 1.0 / Math.sqrt(Math.pow(x_m - x_i, 2) + Math.pow(y_m - y_i, 2));
+        let dx = kcolm[i] * ((x_m - x_i) - lcolm[i] * (x_m - x_i) * denominator);
+        let dy = kcolm[i] * ((y_m - y_i) - lcolm[i] * (y_m - y_i) * denominator);
+        colm[iIdx] = [dx, dy];
+        dE_dx += dx;
+        dE_dy += dy;
 
+        //add new energy to sum of each column
+        let sum = this.E_sums[i];
+        sum[0] += (dx-oldDx);
+        sum[1] += (dy-oldDy);
+      }
+    }
+    //Store sum at -1 index
+    this.E_sums[m] = [dE_dx, dE_dy];
+  }
 }
 
 export default KamadaKawai;

lib/network/modules/LayoutEngine.js

@@ -161,9 +161,9 @@ class LayoutEngine {
   positionInitially(nodesArray) {
     if (this.options.hierarchical.enabled !== true) {
       this.randomSeed = this.initialRandomSeed;
+      let radius = nodesArray.length + 50;
       for (let i = 0; i < nodesArray.length; i++) {
         let node = nodesArray[i];
-        let radius = 10 * 0.1 * nodesArray.length + 10;
         let angle = 2 * Math.PI * this.seededRandom();
         if (node.x === undefined) {
           node.x = radius * Math.cos(angle);
@@ -196,34 +196,46 @@ class LayoutEngine {
       if (positionDefined < 0.5 * this.body.nodeIndices.length) {
         let MAX_LEVELS = 10;
         let level = 0;
-        let clusterThreshold = 100;
+        let clusterThreshold = 150;
+        //Performance enhancement, during clustering edges need only be simple straight lines. These options don't propagate outside the clustering phase.
+        let clusterOptions = {
+          clusterEdgeProperties:{
+            smooth: {
+              enabled: false
+            }
+          }
+        };
+
         // if there are a lot of nodes, we cluster before we run the algorithm.
         if (this.body.nodeIndices.length > clusterThreshold) {
           let startLength = this.body.nodeIndices.length;
-          while (this.body.nodeIndices.length > clusterThreshold) {
+          while (this.body.nodeIndices.length > clusterThreshold && level <= MAX_LEVELS) {
             //console.time("clustering")
             level += 1;
             let before = this.body.nodeIndices.length;
             // if there are many nodes we do a hubsize cluster
             if (level % 3 === 0) {
-              this.body.modules.clustering.clusterBridges();
+              this.body.modules.clustering.clusterBridges(clusterOptions);
             }
             else {
-              this.body.modules.clustering.clusterOutliers();
+              this.body.modules.clustering.clusterOutliers(clusterOptions);
             }
             let after = this.body.nodeIndices.length;
-            if ((before == after && level % 3 !== 0) || level > MAX_LEVELS) {
+            if (before == after && level % 3 !== 0) {
               this._declusterAll();
               this.body.emitter.emit("_layoutFailed");
               console.info("This network could not be positioned by this version of the improved layout algorithm. Please disable improvedLayout for better performance.");
               return;
             }
             //console.timeEnd("clustering")
-            //console.log(level,after)
+            //console.log(before,level,after);
           }
           // increase the size of the edges
           this.body.modules.kamadaKawai.setOptions({springLength: Math.max(150, 2 * startLength)})
         }
+        if (level > MAX_LEVELS){
+          console.info("The clustering didn't succeed within the amount of interations allowed, progressing with partial result.");
+        }
 
         // position the system for these nodes and edges
         this.body.modules.kamadaKawai.solve(this.body.nodeIndices, this.body.edgeIndices, true);

lib/network/modules/components/algorithms/FloydWarshall.js

@@ -4,7 +4,8 @@
 
 
 class FloydWarshall {
-  constructor(){}
+  constructor() {
+  }
 
   getDistances(body, nodesArray, edgesArray) {
     let D_matrix = {};
@@ -12,11 +13,11 @@ class FloydWarshall {
 
     // prepare matrix with large numbers
     for (let i = 0; i < nodesArray.length; i++) {
-      D_matrix[nodesArray[i]] = {};
-      D_matrix[nodesArray[i]] = {};
+      let node = nodesArray[i];
+      let cell = {};
+      D_matrix[node] = cell;
       for (let j = 0; j < nodesArray.length; j++) {
-        D_matrix[nodesArray[i]][nodesArray[j]] = (i == j ? 0 : 1e9);
-        D_matrix[nodesArray[i]][nodesArray[j]] = (i == j ? 0 : 1e9);
+        cell[nodesArray[j]] = (i == j ? 0 : 1e9);
       }
     }
 
@@ -34,10 +35,18 @@ class FloydWarshall {
 
     // Adapted FloydWarshall based on unidirectionality to greatly reduce complexity.
     for (let k = 0; k < nodeCount; k++) {
-      for (let i = 0; i < nodeCount-1; i++) {
-        for (let j = i+1; j < nodeCount; j++) {
-          D_matrix[nodesArray[i]][nodesArray[j]] = Math.min(D_matrix[nodesArray[i]][nodesArray[j]],D_matrix[nodesArray[i]][nodesArray[k]] + D_matrix[nodesArray[k]][nodesArray[j]])
-          D_matrix[nodesArray[j]][nodesArray[i]] = D_matrix[nodesArray[i]][nodesArray[j]];
+      let knode = nodesArray[k];
+      let kcolm = D_matrix[knode];
+      for (let i = 0; i < nodeCount - 1; i++) {
+        let inode = nodesArray[i];
+        let icolm = D_matrix[inode];
+        for (let j = i + 1; j < nodeCount; j++) {
+          let jnode = nodesArray[j];
+          let jcolm = D_matrix[jnode];
+
+          let val = Math.min(icolm[jnode], icolm[knode] + kcolm[jnode]);
+          icolm[jnode] = val;
+          jcolm[inode] = val;
         }
       }
     }