Fix node sampling for the background.

Previous node sampling was a heuristic that may loop infinitely.
Now using proper CDF sampling. Corrected labels, we compute a MST
not a Steiner tree.

templates/bg_graph.html

 <div id="knWrapper">
-  <h4 class="d-konami m-2">Multidirectional Dijkstra background by Spak</h4>
+  <h4 class="d-konami m-2">Multidirectional Spanning Tree by Spak</h4>
   <button type="button" class="btn btn-light m-2 d-konami" data-toggle="modal" data-target="#knCustomizeModal">
     Customize
   </button>

templates/konami.html

@@ -103,7 +103,7 @@
             </div>
           </div>
           <div class="form-group form-row mb-1">
-            <label for="knTrunkCol" class="col text-right col-form-label col-form-label-sm">Steiner tree path color</label>
+            <label for="knTrunkCol" class="col text-right col-form-label col-form-label-sm">Spanning tree path color</label>
             <div class="col-5">
               <input type="text" class="form-control-sm form-control" id="knTrunkCol" value="#444">
             </div>

webpack/js/mlab.js

@@ -4,6 +4,8 @@ import 'bootstrap';
 
 require('typeface-ubuntu');
 
+var bounds = require('binary-search-bounds')
+
 import Konami from 'konami';
 
 const Snap = require( "imports-loader?this=>window,fix=>module.exports=0!snapsvg/dist/snap.svg.js" );
@@ -72,7 +74,12 @@ function paintTree() {
         const dx = FEAS_CENTER[0] - pos[0]
         const dy = FEAS_CENTER[1] - pos[1]
         const l2 = Math.sqrt(dx * dx + dy * dy)
-        const unit_l2 = Math.max(Math.min((l2 - FEAS_RAD) / FEAS_FALLOFF, 1.), 0.)
+        let unit_l2 = null
+        if (FEAS_FALLOFF > 0) {
+            unit_l2 = Math.max(Math.min((l2 - FEAS_RAD) / FEAS_FALLOFF, 1.), 0.)
+        } else {
+            unit_l2 = l2 >= FEAS_RAD ? 1. : 0.
+        }
         const l2_pow_law = Math.pow(unit_l2, FEAS_FALLOFF_EXP)
         const rand_lerp = l2_pow_law * (1. - FEAS_RND_FRAC) + FEAS_RND_FRAC * Math.random()
         return rand_lerp
@@ -134,16 +141,24 @@ function paintTree() {
         }
     })
 
+    let cdf = [0.]
+    for (let nodeIdx = 0; nodeIdx < grid.numNodes; nodeIdx++) {
+        cdf.push(cdf[cdf.length - 1] + node_feasibility(nodeIdx)) + 1e-5
+    }
+
     function get_random_unreachable_node() {
         let node = null
-        while (node == null || algo.labels[node].isReachable() || node_feasibility(node) < 0.5) {
-            node = Math.floor(Math.random() * grid.numNodes)
+        while (node == null || algo.labels[node].isReachable()) {
+            // We should not be getting grid.numNodes, but to be safe we upper bound it.
+            node = Math.min(grid.numNodes - 1, bounds.le(cdf, Math.random() * cdf[cdf.length - 1]))
         }
         return node
     }
+
     for (let i = 0; i < N_SOURCES; i++) {
         algo.addSource(get_random_unreachable_node(), true)
     }
+
     const anim = setInterval(function() {
         for (let i = 0; i < LBLS_PER_FRAME; ++i) {
             const result = algo.propagate(true)

webpack/package-lock.json

@@ -822,6 +822,12 @@
       "integrity": "sha512-DYWGk01lDcxeS/K9IHPGWfT8PsJmbXRtRd2Sx72Tnb8pcYZQFF1oSDb8hJtS1vhp212q1Rzi5dUf9+nq0o9UIg==",
       "dev": true
     },
+    "binary-search-bounds": {
+      "version": "2.0.4",
+      "resolved": "https://registry.npmjs.org/binary-search-bounds/-/binary-search-bounds-2.0.4.tgz",
+      "integrity": "sha512-2hg5kgdKql5ClF2ErBcSx0U5bnl5hgS4v7wMnLFodyR47yMtj2w+UAZB+0CiqyHct2q543i7Bi4/aMIegorCCg==",
+      "dev": true
+    },
     "block-stream": {
       "version": "0.0.9",
       "resolved": "https://registry.npmjs.org/block-stream/-/block-stream-0.0.9.tgz",

webpack/package.json

@@ -31,7 +31,8 @@
     "webpack": "^4.25.1",
     "webpack-bundle-analyzer": "^3.0.3",
     "webpack-cli": "^3.1.2",
-    "typeface-ubuntu": "^0.0.65"
+    "typeface-ubuntu": "^0.0.65",
+    "binary-search-bounds": "^2.0.4"
   },
   "dependencies": {
     "@fortawesome/fontawesome": "^1.1.8",