68 lines
1.9 KiB
JavaScript
68 lines
1.9 KiB
JavaScript
"use strict";
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var _ = require("../lodash");
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module.exports = crossCount;
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/*
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* A function that takes a layering (an array of layers, each with an array of
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* ordererd nodes) and a graph and returns a weighted crossing count.
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*
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* Pre-conditions:
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*
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* 1. Input graph must be simple (not a multigraph), directed, and include
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* only simple edges.
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* 2. Edges in the input graph must have assigned weights.
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*
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* Post-conditions:
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*
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* 1. The graph and layering matrix are left unchanged.
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*
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* This algorithm is derived from Barth, et al., "Bilayer Cross Counting."
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*/
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function crossCount(g, layering) {
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var cc = 0;
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for (var i = 1; i < layering.length; ++i) {
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cc += twoLayerCrossCount(g, layering[i-1], layering[i]);
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}
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return cc;
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}
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function twoLayerCrossCount(g, northLayer, southLayer) {
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// Sort all of the edges between the north and south layers by their position
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// in the north layer and then the south. Map these edges to the position of
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// their head in the south layer.
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var southPos = _.zipObject(southLayer,
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_.map(southLayer, function (v, i) { return i; }));
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var southEntries = _.flatten(_.map(northLayer, function(v) {
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return _.sortBy(_.map(g.outEdges(v), function(e) {
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return { pos: southPos[e.w], weight: g.edge(e).weight };
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}), "pos");
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}), true);
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// Build the accumulator tree
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var firstIndex = 1;
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while (firstIndex < southLayer.length) firstIndex <<= 1;
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var treeSize = 2 * firstIndex - 1;
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firstIndex -= 1;
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var tree = _.map(new Array(treeSize), function() { return 0; });
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// Calculate the weighted crossings
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var cc = 0;
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_.forEach(southEntries.forEach(function(entry) {
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var index = entry.pos + firstIndex;
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tree[index] += entry.weight;
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var weightSum = 0;
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while (index > 0) {
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if (index % 2) {
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weightSum += tree[index + 1];
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}
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index = (index - 1) >> 1;
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tree[index] += entry.weight;
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}
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cc += entry.weight * weightSum;
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}));
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return cc;
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}
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