Cost Matrix - Category¶

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

Indices and tables

• Index
• Search Page