Redo the horizontal compaction phase

I continue to come across new cases where the BK horizontal compaction
algorithm fails. Instead of trying to continue to patch it, I've
replaced it entirely with a simpler two-sweep DFS algorithm which works
for all of the failing cases I've tested.

Fixes #125
Fixes #158

Author: zenkyomu

lib/position/bk.js

@@ -1,6 +1,7 @@
 "use strict";
 
 var _ = require("../lodash"),
+    Graph = require("../graphlib").Graph,
     util = require("../util");
 
 /*
@@ -204,74 +205,71 @@ function verticalAlignment(g, layering, conflicts, neighborFn) {
 }
 
 function horizontalCompaction(g, layering, root, align, reverseSep) {
-  // We use local variables for these parameters instead of manipulating the
-  // graph because it becomes more verbose to access them in a chained manner.
-  var shift = {},
-      shiftNeighbor = {},
-      sink = {},
-      xs = {},
-      pred = {},
-      graphLabel = g.graph(),
-      sepFn = sep(graphLabel.nodesep, graphLabel.edgesep, reverseSep);
+  // This portion of the algorithm differs from BK due to a number of problems.
+  // Instead of their algorithm we construct a new block graph and do two
+  // sweeps. The first sweep places blocks with the smallest possible
+  // coordinates. The second sweep removes unused space by moving blocks to the
+  // greatest coordinates without violating separation.
+  var xs = {},
+      blockG = buildBlockGraph(g, layering, root, reverseSep);
+
+  // First pass, assign smallest coordinates via DFS
+  var visited = {};
+  function pass1(v) {
+    if (!_.has(visited, v)) {
+      visited[v] = true;
+      xs[v] = _.reduce(blockG.inEdges(v), function(max, e) {
+        pass1(e.v);
+        return Math.max(max, xs[e.v] + blockG.edge(e));
+      }, 0);
+    }
+  }
+  _.each(blockG.nodes(), pass1);
+
+  function pass2(v) {
+    if (visited[v] !== 2) {
+      visited[v]++;
+      var min = _.reduce(blockG.outEdges(v), function(min, e) {
+        pass2(e.w);
+        return Math.min(min, xs[e.w] - blockG.edge(e));
+      }, Number.POSITIVE_INFINITY);
+      if (min !== Number.POSITIVE_INFINITY) {
+        xs[v] = Math.max(xs[v], min);
+      }
+    }
+  }
+  _.each(blockG.nodes(), pass2);
 
-  _.each(layering, function(layer) {
-    _.each(layer, function(v, order) {
-      sink[v] = v;
-      shift[v] = Number.POSITIVE_INFINITY;
-      pred[v] = layer[order - 1];
-    });
-  });
 
-  _.each(g.nodes(), function(v) {
-    if (root[v] === v) {
-      placeBlock(g, layering, sepFn, root, align, shift, shiftNeighbor, sink, pred, xs, v);
-    }
+  // Assign x coordinates to all nodes
+  _.each(align, function(v) {
+    xs[v] = xs[root[v]];
   });
 
+  return xs;
+}
+
+
+function buildBlockGraph(g, layering, root, reverseSep) {
+  var blockGraph = new Graph(),
+      graphLabel = g.graph(),
+      sepFn = sep(graphLabel.nodesep, graphLabel.edgesep, reverseSep);
+
   _.each(layering, function(layer) {
+    var u;
     _.each(layer, function(v) {
-      xs[v] = xs[root[v]];
-      // This line differs from the source paper. See
-      // http://www.inf.uni-konstanz.de/~brandes/publications/ for details.
-      if (v === root[v] && shift[sink[root[v]]] < Number.POSITIVE_INFINITY) {
-        xs[v] += shift[sink[root[v]]];
-
-        // Cascade shifts as necessary
-        var w = shiftNeighbor[sink[root[v]]];
-        if (w && shift[w] !== Number.POSITIVE_INFINITY) {
-          xs[v] += shift[w];
-        }
+      var vRoot = root[v];
+      blockGraph.setNode(vRoot);
+      if (u) {
+        var uRoot = root[u],
+            prevMax = blockGraph.edge(uRoot, vRoot);
+        blockGraph.setEdge(uRoot, vRoot, Math.max(sepFn(g, v, u), prevMax || 0));
       }
+      u = v;
     });
   });
 
-  return xs;
-}
-
-function placeBlock(g, layering, sepFn, root, align, shift, shiftNeighbor, sink, pred, xs, v) {
-  if (_.has(xs, v)) return;
-  xs[v] = 0;
-
-  var w = v,
-      u;
-  do {
-    if (pred[w]) {
-      u = root[pred[w]];
-      placeBlock(g, layering, sepFn, root, align, shift, shiftNeighbor, sink, pred, xs, u);
-      if (sink[v] === v) {
-        sink[v] = sink[u];
-      }
-
-      var delta = sepFn(g, w, pred[w]);
-      if (sink[v] !== sink[u]) {
-        shift[sink[u]] = Math.min(shift[sink[u]], xs[v] - xs[u] - delta);
-        shiftNeighbor[sink[u]] = sink[v];
-      } else {
-        xs[v] = Math.max(xs[v], xs[u] + delta);
-      }
-    }
-    w = align[w];
-  } while (w !== v);
+  return blockGraph;
 }
 
 /*