pgr_bdastar doesn't return the same result as pgr_astar

[LHBruneton-C2C]

Problem

pgr_bdastar doesn't return the same result as pgr_astar

To Reproduce

Using pgRouting docker image, import the following data:

edge_min_repro.zip

Then run the following queries:

SELECT 
seq, path_seq AS "pathSeq", node, edge, pgr.cost, agg_cost AS "aggCost"
FROM pgr_bdastar('SELECT * FROM edge', 1153548005, 558255664, true) as pgr
ORDER BY seq;

which returns:

1 1 1153548005 54256 0.000379723504336132 0
2 2 558255704 54146 0.000304523536838747 0.000379723504336132
3 3 558255705 54149 0.00138401927422877 0.00068424704117488
4 4 558255703 54142 0.000341445410931827 0.00206826631540365
5 5 558255702 54141 0.00148219733407846 0.00240971172633548
6 6 558255664 -1 0 0.00389190906041394

and

SELECT 
seq, path_seq AS "pathSeq", node, edge, pgr.cost, agg_cost AS "aggCost"
FROM pgr_astar('SELECT * FROM edge', 1153548005, 558255664, true) as pgr
ORDER BY seq;

which returns:

1 1 1153548005 54256 0.00037972350433613237 0
2 2 558255704 54147 0.00027403899672301315 0.00037972350433613237
3 3 1037080644 54145 0.0002883815801048997 0.0006537625010591456
4 4 1037086594 54144 0.0005431804623754474 0.0009421440811640453
5 5 1037074188 54143 0.0003132688487491818 0.0014853245435394926
6 6 558255702 54141 0.001482197334078463 0.0017985933922886744
7 7 558255664 -1 0 0.0032807907263671375

Expectation

Result should be the same, with the same sequence and the same aggCost.

Sample Data

Uploaded above.

Platform/versions

docker images 11-2.5-2.6.2 or 12-3.0-3.1.0 or 13-3.1-3.1.3

[cvvergara]

From the pgr_aStar and pgr_bdAstar documentation
They are comparable with dijkstra when you use heuristic 0

0: h(v) = 0 (Use this value to compare with pgr_dijkstra)

Both should give the same result as pgr_dijkstra, and therefore they give the same result between each other.
They are not comparable between each other or with pgr_dijkstra with a different heuristic that I know of.
If you find a publication that proves that they are comparable, would be nice.
Tests about comparison with pgr_dijkstra:
https://github.com/pgRouting/pgrouting/blob/master/pgtap/bdAstar/bdAstar-compare-dijkstra.sql
https://github.com/pgRouting/pgrouting/blob/master/pgtap/astar/astar_ManyToMany-compare-dijkstra.test.sql

Note of the modification the sample data due to the fact that all edges have the same value 1 for cost and that alone can give different results for pgr_dijkstra in different runs. This change assures that no matter the order of the data, all routes have different values and has a unique solution for a shortest path.

UPDATE edge_table SET cost = sign(cost) + 0.001 * id * id, reverse_cost = sign(reverse_cost) + 0.001 * id * id;

[LHBruneton-C2C]

Thank you @cvvergara for taking the time to answer me !
Indeed, on reading your asnwer, I found out I had misunderstood the pgr_bdAstar documentation. I still thought this was meant to find the shortest path, whatever graph we feed to it. But it would be more appropriate to say that it will find the shortest path, if the graph is homogeneous. Would you say this is more correct ?
Tank you again, and indeed, this wasn't a bug.

[cvvergara]

@LHBruneton-C2C
Marked it as a documentation issue