## Cost Matrix - Category

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.

### 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 $$O( start\_vids * (V \log V + E))$$