PGX 21.1.1

Enumerate Simple Paths

Category path finding

Algorithm ID pgx_builtin_o12_enumerate_simple_paths

Time Complexity O(E * k) with E = number of edges, k <= maximum number of iterations

Space Requirement O(V) with V = number of vertices


Enumerate all simple paths between the source and destination vertex


Input Argument Type Comment
G graph
src node the source vertex.
dst node the destination vertex.
k int the dimension of the distances property; i.e. number of high-degree vertices.
verticesOnPath nodeSet the vertices on the path.
edgesOnPath edgeSet the edges on the path.
f_dist map map containing the distance from the source vertex for each vertex on a path.
Output Argument Type Comment
pathLengths sequence sequence containing the path lengths.
pathVertices nodeSeq vertex-sequence containing the vertices on the paths.
pathEdges edgeSeq edge-sequence containing the edges on the paths.


 * Copyright (C) 2013 - 2020 Oracle and/or its affiliates. All rights reserved.
procedure enumerate_simple_paths(graph G, node src, node dst, int k,
    nodeSet verticesOnPath, edgeSet edgesOnPath, map<node, int> f_dist; sequence<int> pathLengths, nodeSeq pathVertices, edgeSeq pathEdges) {

  // we generate all the paths by doing a pseudo-DFS using a stack
  // (we don't include paths with loops)

  nodeSeq stack;
  sequence<int> hopCountStack;


  map<node, node> parentNodes;
  parentNodes[src] = NIL;
  map<node, edge> parentEdges;
  parentEdges[src] = NIL;

  if (k > 0) {
    while (stack.size() > 0) {
      node cur = stack.pop();
      int hop = hopCountStack.pop();

      if (cur == dst) {
        // write down the path (in reverse order)
        int length = 1;
        node pathVertex = cur;

        edge pathEdge = parentEdges[pathVertex];
        pathVertex = parentNodes[pathVertex];

        int l = hop;
        while (l > 0) {

          // prepare next iteration
          pathEdge = parentEdges[pathVertex];
          pathVertex = parentNodes[pathVertex];


      if (hop < k) {
        // we can do more hops
        int newHop = hop + 1;
        for (m : cur.inOutNbrs) {
          edge e = m.edge();
          // to avoid loops we force increasing distance from the source
          if (verticesOnPath.has(m) && edgesOnPath.has(e) && f_dist[m] <= k && f_dist[cur] < f_dist[m]) {
            parentNodes[m] = cur;
            parentEdges[m] = e;