Cost Matrix - Category¶

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