Cost Matrix - Category

Warning

These are proposed functions for next mayor release.

  • They are not officially in the current release.
  • They will likely officially be part of the next mayor release:
    • The functions make use of ANY-INTEGER and ANY-NUMERICAL
    • Name might not change. (But still can)
    • Signature might not change. (But still can)
    • Functionality might not change. (But still can)
    • pgTap tests have being done. But might need more.
    • Documentation might need refinement.

General Information

Synopsis

Traveling Sales Person - Family of functions needs as input a symmetric cost matrix and no edge (u, v) must value \(\infty\).

This collection of functions will return a cost matrix in form of a table.

Characteristics

The main Characteristics are:

  • Can be used as input to pgr_TSP.

    • directly:when the resulting matrix is symmetric and there is no \(\infty\) value.

    • It will be the users responsibility to make the matrix symmetric.

      • By using geometric or harmonic average of the non symmetric values.
      • By using max or min the non symmetric values.
      • By setting the upper triangle to be the mirror image of the lower triangle.
      • By setting the lower triangle to be the mirror image of the upper triangle.

    • It is also the users responsibility to fix an \(\infty\) value.

  • Each function works as part of the family it belongs to.

  • It does not return a path.

  • Returns the sum of the costs of the shortest path for pair combination of nodes in the graph.

  • Process is done only on edges with positive costs.

  • Values are returned when there is a path.

    • The returned values are in the form of a set of (start_vid, end_vid, agg_cost).
    • When the starting vertex and ending vertex are the same, there is no path.
      • The agg_cost int the non included values (v, v) is 0.
    • When the starting vertex and ending vertex are the different and there is no path.
      • The agg_cost in the non included values (u, v) is \(\infty\).

  • Let be the case the values returned are stored in a table, so the unique index would be the pair: (start_vid, end_vid).

  • Depending on the function and its parameters, the results can be symmetric.

    • The agg_cost of (u, v) is the same as for (v, u).

  • Any duplicated value in the start_vids are ignored.

  • The returned values are ordered:

    • start_vid ascending
    • end_vid ascending

  • Running time: approximately \(O(| start\_vids | * (V \log V + E))\)

See Also

Indices and tables