Modular decomposition bug

[Jori Mäntysalo]

sage: G1 = Graph('FwA]w')
sage: G2 = Graph('F@Nfg')
sage: G1.modular_decomposition(algorithm='tedder')
(PRIME, [6, 2, 1, 5, 0, (PARALLEL, [3, 4])])
sage: G2.modular_decomposition(algorithm='tedder')
(PRIME, [6, 5, 0, 2, 3, 1, 4])
sage: G1.is_isomorphic(G2)
True

#24898 was not enough.

This ticket removes 'tedder' implementation, as buggy unfixable abandonware (see #33902 for another example of a bug); the algorithm= option is made into a no-op, to be removed after the deprecation period, as we only have one implementation now.

[David Coudert]

That's certainly not an easy issue to fix. I have not clue what's going on :(

[Jori Mäntysalo]

I don't know if this helps, but I was cross-checking #25763 and it seems that the bug is not visible with

P._hasse_diagram.transitive_closure().to_undirected().is_prime()

where P is any poset. In the internal digraph we have consecutive integers as vertices and 0, 1, ..., n-1 is a topological sort of the digraph.

[David Coudert]

I tried other labelings of the graph and its working correctly when the first vertex of G.vertex_iterator() is not involved in the parallel node.

sage: G3 = Graph('F|NE?')
sage: G3.modular_decomposition()
(PRIME, [2, (PARALLEL, [5, 6]), 1, 3, 0, 4])

With 'G2', the construction starts from vertex 0 that should be in a parallel node (PARALLEL, [0, 1]). If I add a twin to vertex 4, the new parallel node is detected.

sage: G2.add_edges([(2,7), (3,7)])
sage: G2.modular_decomposition()
(PRIME, [6, 5, 0, 2, 3, 1, (PARALLEL, [4, 7])])

[Lokesh Jain]

I have pushed the changes which were required to fix the bug. The change required was to remove the is_separated field from Node class in modular_decomposition.py. It removes the optimization which was causing the bug.

---

New commits:

​b71307d

trac #25872: Remove is_separated instance variable from Node class in modular_decomposition.py

[David Coudert]

Thank you Lokesh.

You must add the following tests to the TESTS block of method modular_decomposition to show that the issue is fixed.

Ticket :trac:`25872` is fixed::

    sage: G1 = Graph('FwA]w')
    sage: G2 = Graph('F@Nfg')
    sage: G1.is_isomorphic(G2)
    True
    sage: G1.modular_decomposition()
    (PRIME, [6, 2, 1, 5, 0, (PARALLEL, [3, 4])])
    sage: G2.modular_decomposition()
    (PRIME, [6, 5, (PARALLEL, [0, 1]), 2, 3, 4])
    sage: G2.add_edges([(2,7), (3,7)])
    sage: G2.modular_decomposition()
    (PRIME, [6, 5, (PARALLEL, [0, 1]), 2, 3, (PARALLEL, [4, 7])])

[Jori Mäntysalo]

Still doesn't work.

sage: a = Graph('PdDoIHG?o@OeC?_BsWCSsI?c')
sage: b = a.canonical_label()
sage: a.is_prime(), b.is_prime()
(True, False)

Found by

set_random_seed(0)
for i in xrange(10^3):
    G1 = graphs.RandomGNP(17, 0.3)
    G2 = G1.canonical_label()
    if G1.is_prime() != G2.is_prime():
        print(i)
        G1.show()
        break
else:
    print("OK")

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​672a110

trac #25872: Added tests in graph.py#modular_decomposition

[Lokesh Jain]

Replying to jmantysalo:

Still doesn't work.

Thanks for posting the example. Let me take a look.

[David Einstein]

A few questions.

Would it be of use to add an algorithm parameter to modular_decomposition and is_prime? I have code for the O(n³) algorithm of [Habib and Maurer 1979] that is probably slower than the current code, but seems to work. Should I attempt to integrate it, and if so should I do it in this ticket or start a new one?

Should we move modular_decomposition.py into the src/sage/graphs/graph_decompositions directory?

In the testing section of modular_decomposition.py the function children_node_type is used to flag an error if all of the children of a SERIES or PARALLEL node are of the same type as their parent. I think that this is too loose and an error should be noted if any of the children have the same type as their parents, otherwise the condition that nodes in the tree represent maximal modules is violated.

[David Coudert]

This is a very good idea to add another algorithm and the parameter algorithm if it helps checking the validity of both algorithms. A slow algorithm is OK in such case. However, it should be done in a separate ticket.

It is possible to move the file to src/sage/graphs/graph_decompositions while working on the new ticket.

[David Einstein]

I added trac #26496. The code there should be functional if you add algorithm='habib' to each call to modular_decomposition or is_prime.

[Dima Pasechnik]

see also #33902

How about removing 'tedder' completely?

[David Coudert]

I can only agree with that. The code is buggy and I don't know how to fix that.

[Dima Pasechnik]

OK, I'll try doing this.

[David Coudert]

We can at least start with a deprecation warning.

[Dima Pasechnik]

New commits:

​c7e8063

remove buggy 'tedder' modular decomposition

[Dima Pasechnik]

As it's buggy, no need for deprecation, IMHO

[David Coudert]

This looks good, but In graph.py, we should add the ticket number to the note explaining that we removed a buggy algorithm

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​22f15f5

mention trac ticket number

[Dima Pasechnik]

Replying to dcoudert:

This looks good, but In graph.py, we should add the ticket number to the note explaining that we removed a buggy algorithm

done

[David Coudert]

Thank you Dima.

LGTM.

[David Coudert]

We should certainly update the ticket description to reflect the removal.

[Matthias Köppe]

the algorithm= option is removed, as we only have one implementation now.

This breaks existing code

[David Coudert]

So what should we do ? deprecate this option before removing tedder in a year ? remove tedder now and let this parameter even if unused with a deprecation ? something else ?

[Matthias Köppe]

Just make it so that passing algorithm='habib' does not become an error

[Dima Pasechnik]

algorithm='tedder' should be an error now.

The problem is, however, not limited to this, as there is also a modular_decomposition(foo) function, which was equivalent to foo.modular_decomposition(algorithm='tedder'). In the present branch modular_decomposition(foo) became equivalent to the (old) foo.modular_decomposition(algorithm='habib'), because, what else?

I think it's too much fuss to fiddle around with deprecations here.

[Matthias Köppe]

Just don't make these breaking API changes:

--- a/src/sage/graphs/graph.py
+++ b/src/sage/graphs/graph.py
@@ -7574,7 +7574,7 @@ class Graph(GenericGraph):
             return list(core.values())
 
     @doc_index("Leftovers")
-    def modular_decomposition(self, algorithm='habib', style='tuple'):
+    def modular_decomposition(self, style='tuple'):
         r"""
         Return the modular decomposition of the current graph.
 
@@ -8035,23 +8014,13 @@ class Graph(GenericGraph):
         return self.planar_dual().is_circumscribable(solver=solver, verbose=verbose)
 
     @doc_index("Graph properties")
-    def is_prime(self, algorithm='habib'):
+    def is_prime(self):
         r"""
         Test whether the current graph is prime.
 

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​f610e5a

retained 'algorithm=' with deprecation

[Matthias Köppe]

LGTM, thanks.