@antv/layout/src/algorithm/antv-dagre/order/cross-count.ts

graph layout algorithm

/*
 * A function that takes a layering (an array of layers, each with an array of
 * ordererd nodes) and a graph and returns a weighted crossing count.
 *
 * Pre-conditions:
 *
 *    1. Input graph must be simple (not a multigraph), directed, and include
 *       only simple edges.
 *    2. Edges in the input graph must have assigned weights.
 *
 * Post-conditions:
 *
 *    1. The graph and layering matrix are left unchanged.
 *
 * This algorithm is derived from Barth, et al., "Bilayer Cross Counting."
 */

import type { ID } from '../../../types';
import { DagreGraph } from '../graph';
import { zipObject } from '../util';

const twoLayerCrossCount = (
  g: DagreGraph,
  northLayer: ID[],
  southLayer: ID[],
) => {
  // Sort all of the edges between the north and south layers by their position
  // in the north layer and then the south. Map these edges to the position of
  // their head in the south layer.
  const southPos = zipObject(
    southLayer,
    southLayer.map((v, i) => i),
  );
  const unflat = northLayer.map((v) => {
    const unsort = g.getRelatedEdges(v, 'out').map((e) => {
      return { pos: southPos[e.target] || 0, weight: e.data.weight };
    });
    return unsort?.sort((a, b) => a.pos - b.pos);
  });
  const southEntries = unflat.flat().filter((entry) => entry !== undefined);

  // Build the accumulator tree
  let firstIndex = 1;
  while (firstIndex < southLayer.length) firstIndex <<= 1;
  const treeSize = 2 * firstIndex - 1;
  firstIndex -= 1;
  const tree = Array(treeSize).fill(0, 0, treeSize);

  // Calculate the weighted crossings
  let cc = 0;
  southEntries?.forEach((entry) => {
    if (entry) {
      let index = entry.pos + firstIndex;
      tree[index] += entry.weight;
      let weightSum = 0;
      while (index > 0) {
        if (index % 2) {
          weightSum += tree[index + 1];
        }
        index = (index - 1) >> 1;
        tree[index] += entry.weight;
      }
      cc += entry.weight! * weightSum;
    }
  });

  return cc;
};

export const crossCount = (g: DagreGraph, layering: ID[][]) => {
  let cc = 0;
  for (let i = 1; i < layering?.length; i += 1) {
    cc += twoLayerCrossCount(g, layering[i - 1], layering[i]);
  }
  return cc;
};