is_directed_acyclic is Cython (--> without NetworX) and its certificates

[ncohen]

This patch contains an Cython implementation of a method testing whether a given digraph is acyclic. If it is, the method returns a topological sort, and returns a circuit otherwise. The method is then called through current Sage methods which relied on NetworkX

def random_acyclic(n, p):
...    g = graphs.RandomGNP(n, p)
...    h = DiGraph()
...    h.add_edges([ ((u,v) if u<v else (v,u)) for u,v,_ in g.edges() ])
...    return h

Before :

sage: g = random_acyclic(100, .2)
sage: %timeit g.is_directed_acyclic()
125 loops, best of 3: 6.54 ms per loop
sage: g = random_acyclic(100, .2)
sage: %timeit g.is_directed_acyclic()
125 loops, best of 3: 6.79 ms per loop
sage: g = random_acyclic(100, .2)
sage: %timeit g.is_directed_acyclic()
125 loops, best of 3: 6.72 ms per loop
sage: g = random_acyclic(100, .2)
sage: %timeit g.is_directed_acyclic()
125 loops, best of 3: 6.96 ms per loop

After :

sage: g = random_acyclic(100, .2)
sage: %timeit g.is_directed_acyclic()
625 loops, best of 3: 376 µs per loop
sage: g = random_acyclic(100, .2)
sage: %timeit g.is_directed_acyclic()
625 loops, best of 3: 375 µs per loop
sage: g = random_acyclic(100, .2)
sage: %timeit g.is_directed_acyclic()
625 loops, best of 3: 388 µs per loop
sage: g = random_acyclic(100, .2)
sage: %timeit g.is_directed_acyclic()
625 loops, best of 3: 380 µs per loop
sage: g = random_acyclic(100, .2)
sage: %timeit g.is_directed_acyclic()
625 loops, best of 3: 383 µs per loop
sage: g = random_acyclic(100, .2)
sage: %timeit g.is_directed_acyclic()
625 loops, best of 3: 380 µs per loop

Nathann

Requires #10435

[ncohen]

updated to pass -testall.. This code was actually used in many places ! I hope they'll like the speedup :-)

Nathann

[rlm]

Looks very good.

Keep Cythonizing graph theory! :)

[jdemeyer]

Line 791 of sage/graphs/digraphs.py should be EXAMPLES:

[ncohen]

Done.

Nathann