# pgRouting Manual (3.1)

## Cost Matrix - Category

- pgr_aStarCostMatrix

- pgr_dijkstraCostMatrix

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.

- pgr_withPointsCostMatrix - proposed

Previous versions of this page

- Supported versions: current(3.1) 3.0 2.6

- Unsupported versions: 2.5 2.4

## 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

- Traveling Sales Person - Family of functions

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