# Cost Matrix¶

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¶

### Sinopsis¶

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