k-shortest-path/index.js

Computes the K shortest paths in a graph from node s to node t using Yen's algorithm

const graphlib = require('graphlib');

exports.ksp = function (g, source, target, K, weightFunc, edgeFunc) {

    // clone graph to avoid changes to the original
    let _g = graphlib.json.read(graphlib.json.write(g));

    // Initialize containers for candidate paths and k shortest paths
    let ksp = [];
    let candidates = [];

    // Compute and add the shortest path */
    let kthPath = getDijkstra(_g, source, target, weightFunc, edgeFunc);
    if (!kthPath) {
        return ksp;
    }
    ksp.push(kthPath);

    // Iteratively compute each of the k shortest paths */
    for (let k = 1; k < K; k++) {

        // Get the (k-1)st shortest path
        let previousPath = cloneObject(ksp[k - 1]); // clone path to new var

        if (!previousPath) {
            break;
        }
        /* Iterate over all of the nodes in the (k-1)st shortest path except for the target node; for each node,
        (up to) one new candidate path is generated by temporarily modifying the graph and then running
        Dijkstra's algorithm to find the shortest path between the node and the target in the modified
        graph */

        for (let i = 0; i < previousPath.edges.length; i++) {


            // Initialize a container to store the modified (removed) edges for this node/iteration
            let removedEdges = [];

            // Spur node = currently visited node in the (k-1)st shortest path
            let spurNode = previousPath.edges[i].fromNode;

            // Root path = prefix portion of the (k-1)st path up to the spur node
            let rootPath = clonePathTo(previousPath, i);

            // Iterate over all of the (k-1) shortest paths */
            ksp.forEach(p => {
                p = cloneObject(p); // clone p
                let stub = clonePathTo(p, i);

                // Check to see if this path has the same prefix/root as the (k-1)st shortest path
                if (isPathEqual(rootPath, stub)) {
                    // If so, eliminate the next edge in the path from the graph (later on, this forces the spur
                    // node to connect the root path with an un-found suffix path) */
                    let re = p.edges[i];
                    _g.removeEdge(re.fromNode, re.toNode);
                    removedEdges.push(re);
                }
            })

            // Temporarily remove all of the nodes in the root path, other than the spur node, from the graph */
            rootPath.edges.forEach(rootPathEdge => {
                let rn = rootPathEdge.fromNode;
                if (rn !== spurNode) {
                    // remove node and return removed edges
                    let removedEdgeFromNode = removeNode(_g, rn, weightFunc);
                    removedEdges.push(...removedEdgeFromNode);
                }
            })

            // Spur path = shortest path from spur node to target node in the reduced graph
            let spurPath = getDijkstra(_g, spurNode, target, weightFunc, edgeFunc);

            // If a new spur path was identified...
            if (spurPath != null) {
                // Concatenate the root and spur paths to form the new candidate path
                let totalPath = cloneObject(rootPath);
                let edgesToAdd = cloneObject(spurPath.edges);
                totalPath.edges.push(...edgesToAdd);
                totalPath.totalCost += spurPath.totalCost;

                // If candidate path has not been generated previously, add it
                if (!isPathExistInArray(candidates, totalPath)) {
                    candidates.push(totalPath);
                }
            }

            addEdges(_g, removedEdges);
        }

        // Identify the candidate path with the shortest cost */
        let isNewPath;
        do {
            kthPath = removeBestCandidate(candidates);
            isNewPath = true;
            if (kthPath != null) {
                for (let p of ksp) {
                    // Check to see if this candidate path duplicates a previously found path
                    if (isPathEqual(p, kthPath)) {
                        isNewPath = false;
                        break;
                    }
                }

            }
        } while (!isNewPath);

        // If there were not any more candidates, stop
        if (kthPath == null) {
            break;
        }

        // Add the best, non-duplicate candidate identified as the k shortest path
        ksp.push(kthPath);
    }
    return ksp;
}


// Dijkstra algorithm to find the shortest path
function getDijkstra(g, source, target, weightFunc, edgeFunc) {
    if (!weightFunc) {
        weightFunc = (e) => g.edge(e);
    }

    let dijkstra = graphlib.alg.dijkstra(g, source, weightFunc, edgeFunc);
    return extractPathFromDijkstra(g, dijkstra, source, target, weightFunc, edgeFunc);
}

function extractPathFromDijkstra(g, dijkstra, source, target, weightFunc, edgeFunc) {
    // check if there is a valid path
    if (dijkstra[target].distance === Number.POSITIVE_INFINITY) {
        return null;
    }

    let edges = [];
    let currentNode = target;
    while (currentNode !== source) {
        let previousNode = dijkstra[currentNode].predecessor;

        // extract weight from edge, using weightFunc if supplied, or the default way
        let weightValue;
        if (weightFunc) {
            weightValue = weightFunc({ v: previousNode, w: currentNode });
        } else {
            weightValue = g.edge(previousNode, currentNode)
        }
        let edge = getNewEdge(previousNode, currentNode, weightValue);
        edges.push(edge);
        currentNode = previousNode;
    }

    let result = {
        totalCost: dijkstra[target].distance,
        edges: edges.reverse()
    };
    return result;
}

function addEdges(g, edges) {
    edges.forEach(e => {
        g.setEdge(e.fromNode, e.toNode, e.edgeObj);
    })
}

// input: a graph and a node to remove
// return value: array of removed edges
function removeNode(g, rn, weightFunc) {

    let remEdges = [];
    let edges = cloneObject(g.edges());
    // save all the edges we are going to remove
    edges.forEach(edge => {
        if (edge.v == rn || edge.w == rn) {

            // extract weight
            let weightValue;
            if (weightFunc) {
                weightValue = weightFunc(edge);
            } else {
                weightValue = g.edge(edge);
            }

            let e = getNewEdge(edge.v, edge.w, weightValue);
            remEdges.push(e);
        }
    })
    g.removeNode(rn); // removing the node from the graph
    return remEdges;
}

// return a new path object from source path to a given index
function clonePathTo(path, i) {
    let newPath = cloneObject(path);
    let edges = [];
    let l = path.edges.length;
    if (i > l) {
        i = 1;
    }
    // copy i edges from the source path
    for (let j = 0; j < i; j++) {
        edges.push(path.edges[j]);
    }

    // calc the cost of the new path
    newPath.totalCost = 0;
    edges.forEach(edge => {
        newPath.totalCost += edge.weight;
    })
    newPath.edges = edges;
    return newPath;
}


// compare between two path objects, return true if equals
function isPathEqual(path1, path2) {
    if (path2 == null) {
        return false;
    }

    let numEdges1 = path1.edges.length;
    let numEdges2 = path2.edges.length;

    // compare number of edges
    if (numEdges1 != numEdges2) {
        return false;
    }

    // compare each edge
    for (let i = 0; i < numEdges1; i++) {
        let edge1 = path1.edges[i];
        let edge2 = path2.edges[i];
        if (edge1.fromNode != edge2.fromNode) {
            return false;
        }
        if (edge1.toNode != edge2.toNode) {
            return false;
        }
    }

    return true;
}

// build a new edge object
function getNewEdge(fromNode, toNode, weight) {
    return {
        fromNode: fromNode,
        toNode: toNode,
        weight: weight
    }
}

// since javascript sends object by ref, we sometimes want to clone objects and its childs to avoid it
// this is a workaround for clone objects
function cloneObject(obj) {
    return JSON.parse(JSON.stringify(obj));
}

// return true if a given path is found on array of path
function isPathExistInArray(candidates, path) {
    candidates.forEach(candi => {
        if (isPathEqual(candi, path)) {
            return true;
        }
    })
    return false;
}

// sort the candidates array by total cose, then remove and return the best candidate.
function removeBestCandidate(candidates) {
    return candidates.sort((a, b) => a.totalCost - b.totalCost).shift();
}