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",