proposed

Warning

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.

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.

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 \(O(| start\_vids | * (V \log V + E))\)