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.npm-cache/_npx/0ebd1cb7ec11dd1f/node_modules/dagre/lib/rank/feasible-tree.js

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+"use strict";
+
+var _ = require("../lodash");
+var Graph = require("../graphlib").Graph;
+var slack = require("./util").slack;
+
+module.exports = feasibleTree;
+
+/*
+ * Constructs a spanning tree with tight edges and adjusted the input node's
+ * ranks to achieve this. A tight edge is one that is has a length that matches
+ * its "minlen" attribute.
+ *
+ * The basic structure for this function is derived from Gansner, et al., "A
+ * Technique for Drawing Directed Graphs."
+ *
+ * Pre-conditions:
+ *
+ *    1. Graph must be a DAG.
+ *    2. Graph must be connected.
+ *    3. Graph must have at least one node.
+ *    5. Graph nodes must have been previously assigned a "rank" property that
+ *       respects the "minlen" property of incident edges.
+ *    6. Graph edges must have a "minlen" property.
+ *
+ * Post-conditions:
+ *
+ *    - Graph nodes will have their rank adjusted to ensure that all edges are
+ *      tight.
+ *
+ * Returns a tree (undirected graph) that is constructed using only "tight"
+ * edges.
+ */
+function feasibleTree(g) {
+  var t = new Graph({ directed: false });
+
+  // Choose arbitrary node from which to start our tree
+  var start = g.nodes()[0];
+  var size = g.nodeCount();
+  t.setNode(start, {});
+
+  var edge, delta;
+  while (tightTree(t, g) < size) {
+    edge = findMinSlackEdge(t, g);
+    delta = t.hasNode(edge.v) ? slack(g, edge) : -slack(g, edge);
+    shiftRanks(t, g, delta);
+  }
+
+  return t;
+}
+
+/*
+ * Finds a maximal tree of tight edges and returns the number of nodes in the
+ * tree.
+ */
+function tightTree(t, g) {
+  function dfs(v) {
+    _.forEach(g.nodeEdges(v), function(e) {
+      var edgeV = e.v,
+        w = (v === edgeV) ? e.w : edgeV;
+      if (!t.hasNode(w) && !slack(g, e)) {
+        t.setNode(w, {});
+        t.setEdge(v, w, {});
+        dfs(w);
+      }
+    });
+  }
+
+  _.forEach(t.nodes(), dfs);
+  return t.nodeCount();
+}
+
+/*
+ * Finds the edge with the smallest slack that is incident on tree and returns
+ * it.
+ */
+function findMinSlackEdge(t, g) {
+  return _.minBy(g.edges(), function(e) {
+    if (t.hasNode(e.v) !== t.hasNode(e.w)) {
+      return slack(g, e);
+    }
+  });
+}
+
+function shiftRanks(t, g, delta) {
+  _.forEach(t.nodes(), function(v) {
+    g.node(v).rank += delta;
+  });
+}

.npm-cache/_npx/0ebd1cb7ec11dd1f/node_modules/dagre/lib/rank/index.js

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+"use strict";
+
+var rankUtil = require("./util");
+var longestPath = rankUtil.longestPath;
+var feasibleTree = require("./feasible-tree");
+var networkSimplex = require("./network-simplex");
+
+module.exports = rank;
+
+/*
+ * Assigns a rank to each node in the input graph that respects the "minlen"
+ * constraint specified on edges between nodes.
+ *
+ * This basic structure is derived from Gansner, et al., "A Technique for
+ * Drawing Directed Graphs."
+ *
+ * Pre-conditions:
+ *
+ *    1. Graph must be a connected DAG
+ *    2. Graph nodes must be objects
+ *    3. Graph edges must have "weight" and "minlen" attributes
+ *
+ * Post-conditions:
+ *
+ *    1. Graph nodes will have a "rank" attribute based on the results of the
+ *       algorithm. Ranks can start at any index (including negative), we'll
+ *       fix them up later.
+ */
+function rank(g) {
+  switch(g.graph().ranker) {
+  case "network-simplex": networkSimplexRanker(g); break;
+  case "tight-tree": tightTreeRanker(g); break;
+  case "longest-path": longestPathRanker(g); break;
+  default: networkSimplexRanker(g);
+  }
+}
+
+// A fast and simple ranker, but results are far from optimal.
+var longestPathRanker = longestPath;
+
+function tightTreeRanker(g) {
+  longestPath(g);
+  feasibleTree(g);
+}
+
+function networkSimplexRanker(g) {
+  networkSimplex(g);
+}

.npm-cache/_npx/0ebd1cb7ec11dd1f/node_modules/dagre/lib/rank/network-simplex.js

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+"use strict";
+
+var _ = require("../lodash");
+var feasibleTree = require("./feasible-tree");
+var slack = require("./util").slack;
+var initRank = require("./util").longestPath;
+var preorder = require("../graphlib").alg.preorder;
+var postorder = require("../graphlib").alg.postorder;
+var simplify = require("../util").simplify;
+
+module.exports = networkSimplex;
+
+// Expose some internals for testing purposes
+networkSimplex.initLowLimValues = initLowLimValues;
+networkSimplex.initCutValues = initCutValues;
+networkSimplex.calcCutValue = calcCutValue;
+networkSimplex.leaveEdge = leaveEdge;
+networkSimplex.enterEdge = enterEdge;
+networkSimplex.exchangeEdges = exchangeEdges;
+
+/*
+ * The network simplex algorithm assigns ranks to each node in the input graph
+ * and iteratively improves the ranking to reduce the length of edges.
+ *
+ * Preconditions:
+ *
+ *    1. The input graph must be a DAG.
+ *    2. All nodes in the graph must have an object value.
+ *    3. All edges in the graph must have "minlen" and "weight" attributes.
+ *
+ * Postconditions:
+ *
+ *    1. All nodes in the graph will have an assigned "rank" attribute that has
+ *       been optimized by the network simplex algorithm. Ranks start at 0.
+ *
+ *
+ * A rough sketch of the algorithm is as follows:
+ *
+ *    1. Assign initial ranks to each node. We use the longest path algorithm,
+ *       which assigns ranks to the lowest position possible. In general this
+ *       leads to very wide bottom ranks and unnecessarily long edges.
+ *    2. Construct a feasible tight tree. A tight tree is one such that all
+ *       edges in the tree have no slack (difference between length of edge
+ *       and minlen for the edge). This by itself greatly improves the assigned
+ *       rankings by shorting edges.
+ *    3. Iteratively find edges that have negative cut values. Generally a
+ *       negative cut value indicates that the edge could be removed and a new
+ *       tree edge could be added to produce a more compact graph.
+ *
+ * Much of the algorithms here are derived from Gansner, et al., "A Technique
+ * for Drawing Directed Graphs." The structure of the file roughly follows the
+ * structure of the overall algorithm.
+ */
+function networkSimplex(g) {
+  g = simplify(g);
+  initRank(g);
+  var t = feasibleTree(g);
+  initLowLimValues(t);
+  initCutValues(t, g);
+
+  var e, f;
+  while ((e = leaveEdge(t))) {
+    f = enterEdge(t, g, e);
+    exchangeEdges(t, g, e, f);
+  }
+}
+
+/*
+ * Initializes cut values for all edges in the tree.
+ */
+function initCutValues(t, g) {
+  var vs = postorder(t, t.nodes());
+  vs = vs.slice(0, vs.length - 1);
+  _.forEach(vs, function(v) {
+    assignCutValue(t, g, v);
+  });
+}
+
+function assignCutValue(t, g, child) {
+  var childLab = t.node(child);
+  var parent = childLab.parent;
+  t.edge(child, parent).cutvalue = calcCutValue(t, g, child);
+}
+
+/*
+ * Given the tight tree, its graph, and a child in the graph calculate and
+ * return the cut value for the edge between the child and its parent.
+ */
+function calcCutValue(t, g, child) {
+  var childLab = t.node(child);
+  var parent = childLab.parent;
+  // True if the child is on the tail end of the edge in the directed graph
+  var childIsTail = true;
+  // The graph's view of the tree edge we're inspecting
+  var graphEdge = g.edge(child, parent);
+  // The accumulated cut value for the edge between this node and its parent
+  var cutValue = 0;
+
+  if (!graphEdge) {
+    childIsTail = false;
+    graphEdge = g.edge(parent, child);
+  }
+
+  cutValue = graphEdge.weight;
+
+  _.forEach(g.nodeEdges(child), function(e) {
+    var isOutEdge = e.v === child,
+      other = isOutEdge ? e.w : e.v;
+
+    if (other !== parent) {
+      var pointsToHead = isOutEdge === childIsTail,
+        otherWeight = g.edge(e).weight;
+
+      cutValue += pointsToHead ? otherWeight : -otherWeight;
+      if (isTreeEdge(t, child, other)) {
+        var otherCutValue = t.edge(child, other).cutvalue;
+        cutValue += pointsToHead ? -otherCutValue : otherCutValue;
+      }
+    }
+  });
+
+  return cutValue;
+}
+
+function initLowLimValues(tree, root) {
+  if (arguments.length < 2) {
+    root = tree.nodes()[0];
+  }
+  dfsAssignLowLim(tree, {}, 1, root);
+}
+
+function dfsAssignLowLim(tree, visited, nextLim, v, parent) {
+  var low = nextLim;
+  var label = tree.node(v);
+
+  visited[v] = true;
+  _.forEach(tree.neighbors(v), function(w) {
+    if (!_.has(visited, w)) {
+      nextLim = dfsAssignLowLim(tree, visited, nextLim, w, v);
+    }
+  });
+
+  label.low = low;
+  label.lim = nextLim++;
+  if (parent) {
+    label.parent = parent;
+  } else {
+    // TODO should be able to remove this when we incrementally update low lim
+    delete label.parent;
+  }
+
+  return nextLim;
+}
+
+function leaveEdge(tree) {
+  return _.find(tree.edges(), function(e) {
+    return tree.edge(e).cutvalue < 0;
+  });
+}
+
+function enterEdge(t, g, edge) {
+  var v = edge.v;
+  var w = edge.w;
+
+  // For the rest of this function we assume that v is the tail and w is the
+  // head, so if we don't have this edge in the graph we should flip it to
+  // match the correct orientation.
+  if (!g.hasEdge(v, w)) {
+    v = edge.w;
+    w = edge.v;
+  }
+
+  var vLabel = t.node(v);
+  var wLabel = t.node(w);
+  var tailLabel = vLabel;
+  var flip = false;
+
+  // If the root is in the tail of the edge then we need to flip the logic that
+  // checks for the head and tail nodes in the candidates function below.
+  if (vLabel.lim > wLabel.lim) {
+    tailLabel = wLabel;
+    flip = true;
+  }
+
+  var candidates = _.filter(g.edges(), function(edge) {
+    return flip === isDescendant(t, t.node(edge.v), tailLabel) &&
+           flip !== isDescendant(t, t.node(edge.w), tailLabel);
+  });
+
+  return _.minBy(candidates, function(edge) { return slack(g, edge); });
+}
+
+function exchangeEdges(t, g, e, f) {
+  var v = e.v;
+  var w = e.w;
+  t.removeEdge(v, w);
+  t.setEdge(f.v, f.w, {});
+  initLowLimValues(t);
+  initCutValues(t, g);
+  updateRanks(t, g);
+}
+
+function updateRanks(t, g) {
+  var root = _.find(t.nodes(), function(v) { return !g.node(v).parent; });
+  var vs = preorder(t, root);
+  vs = vs.slice(1);
+  _.forEach(vs, function(v) {
+    var parent = t.node(v).parent,
+      edge = g.edge(v, parent),
+      flipped = false;
+
+    if (!edge) {
+      edge = g.edge(parent, v);
+      flipped = true;
+    }
+
+    g.node(v).rank = g.node(parent).rank + (flipped ? edge.minlen : -edge.minlen);
+  });
+}
+
+/*
+ * Returns true if the edge is in the tree.
+ */
+function isTreeEdge(tree, u, v) {
+  return tree.hasEdge(u, v);
+}
+
+/*
+ * Returns true if the specified node is descendant of the root node per the
+ * assigned low and lim attributes in the tree.
+ */
+function isDescendant(tree, vLabel, rootLabel) {
+  return rootLabel.low <= vLabel.lim && vLabel.lim <= rootLabel.lim;
+}

.npm-cache/_npx/0ebd1cb7ec11dd1f/node_modules/dagre/lib/rank/util.js

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+"use strict";
+
+var _ = require("../lodash");
+
+module.exports = {
+  longestPath: longestPath,
+  slack: slack
+};
+
+/*
+ * Initializes ranks for the input graph using the longest path algorithm. This
+ * algorithm scales well and is fast in practice, it yields rather poor
+ * solutions. Nodes are pushed to the lowest layer possible, leaving the bottom
+ * ranks wide and leaving edges longer than necessary. However, due to its
+ * speed, this algorithm is good for getting an initial ranking that can be fed
+ * into other algorithms.
+ *
+ * This algorithm does not normalize layers because it will be used by other
+ * algorithms in most cases. If using this algorithm directly, be sure to
+ * run normalize at the end.
+ *
+ * Pre-conditions:
+ *
+ *    1. Input graph is a DAG.
+ *    2. Input graph node labels can be assigned properties.
+ *
+ * Post-conditions:
+ *
+ *    1. Each node will be assign an (unnormalized) "rank" property.
+ */
+function longestPath(g) {
+  var visited = {};
+
+  function dfs(v) {
+    var label = g.node(v);
+    if (_.has(visited, v)) {
+      return label.rank;
+    }
+    visited[v] = true;
+
+    var rank = _.min(_.map(g.outEdges(v), function(e) {
+      return dfs(e.w) - g.edge(e).minlen;
+    }));
+
+    if (rank === Number.POSITIVE_INFINITY || // return value of _.map([]) for Lodash 3
+        rank === undefined || // return value of _.map([]) for Lodash 4
+        rank === null) { // return value of _.map([null])
+      rank = 0;
+    }
+
+    return (label.rank = rank);
+  }
+
+  _.forEach(g.sources(), dfs);
+}
+
+/*
+ * Returns the amount of slack for the given edge. The slack is defined as the
+ * difference between the length of the edge and its minimum length.
+ */
+function slack(g, e) {
+  return g.node(e.w).rank - g.node(e.v).rank - g.edge(e).minlen;
+}