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

See Also¶

• pgr_TSP

Indices and tables

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