gbuoy/lib/data/graph.ts

import { intersect } from "./set"

export type Graph<V> = {
    numVertices: number,
    numEdges: number,
    vertices: {
        [v: string]: V
    },
    edges: {
        [v: string]: Set<string>
    }
}

export type AddVertex<V> = (name: string, v: V) => void
export type AddEdge = (source: string, dest: string) => void

export const createGraph = <V>(cons: (v: AddVertex<V>, e: AddEdge) => void): Graph<V> => {
    const g: Graph<V> = { numVertices: 0, numEdges: 0, vertices: {}, edges: {} }

    const addVertex = (name: string, v: V) => {
        if (typeof g.vertices[name] !== "undefined") {
            return
        }

        g.vertices[name] = v
        g.edges[name] = new Set()
        g.numVertices++
    }

    const addEdge = (source: string, dest: string) => {
        if (typeof g.vertices[source] === "undefined") {
            throw new Error(`vertex \`${source}' does not exist in graph`)
        } else if (typeof g.vertices[dest] === "undefined") {
            throw new Error(`vertex \`${dest}' does not exist in graph`)
        }

        g.edges[source].add(dest)
        g.edges[dest].add(source)
        g.numEdges++
    }

    cons(addVertex, addEdge)

    return g
}

export const neighbors = <V>(g: Graph<V>, name: string): Set<string> => {
    if (typeof g.vertices[name] === "undefined") {
        throw new Error(`vertex \`${name}' does not exist in graph`)
    }

    return g.edges[name]
}

export const vertices = <V>(g: Graph<V>): Set<string> => new Set(Object.keys(g.vertices))

export const edgeConnects = <V>(g: Graph<V>, v1: string, v2: string): boolean => g.edges[v1].has(v2)

export const maxCardinalitySearch = <V>(g: Graph<V>): Array<string> => {
    const weights: { [s: string]: number } = {}
    const ordering: Array<string> = []

    const W = vertices(g)
    const numVertices = W.size

    for (let i = 0; i < numVertices; ++i) {
        const v = findMaxWeight(weights, W)
        ordering.push(v)

        intersect(W, neighbors(g, v)).forEach(x =>
            weights[x] = (weights[x] || 0) + 1
        )

        W.delete(v)
    }

    return ordering
}

const findMaxWeight = (weights: { [s: string]: number }, W: Set<string>): string => {
    let maxV = null
    let maxWeight = -Infinity

    W.forEach(v => {
        const vWeight = weights[v] || 0
        if (vWeight > maxWeight) {
            maxV = v
            maxWeight = vWeight
        }
    })

    if (maxV === null) {
        throw new Error(`remaining vertex set is empty`)
    }

    return maxV
}

export type GraphColoring = {
    numColors: number,
    colors: VertexColoring,
}

export type VertexColoring = {
    [s: string]: number,
}

export const colorGreedy = <V>(g: Graph<V>, vertexOrdering: Array<string>): GraphColoring => {
    if (vertexOrdering.length !== g.numVertices) {
        throw new Error("ordering does not cover all vertices")
    }

    const coloring: GraphColoring = { numColors: 0, colors: {} }
    const usedColors: { [c: number]: boolean } = {}

    vertexOrdering.forEach(v => {
        const ns = neighbors(g, v)

        let color = 0
        while (!colorAvailable(color, ns, coloring.colors)) {
            color++
        }

        coloring.colors[v] = color
        usedColors[color] = true
    })

    coloring.numColors = Object.keys(usedColors).length
    return coloring
}

const colorAvailable = (color: number, neighbors: Set<string>, colors: VertexColoring): boolean => {
    // TODO: Why can't I just iterate over neighbors directly...?
    for (const nbor of Array.from(neighbors)) {
        if (colors[nbor] === color) {
            return false
        }
    }

    return true
}