#17712: Adds memoization to the branch and bound for vertex separation
-------------------------+-------------------------------------------------
Reporter: | Owner:
dcoudert | Status: needs_work
Type: | Milestone: sage-6.5
enhancement | Resolution:
Priority: minor | Merged in:
Component: graph | Reviewers:
theory | Work issues:
Keywords: | Commit:
Authors: David | 4abd2bacff0b06ae13a4fb4d046c7ecee4716d28
Coudert | Stopgaps:
Report Upstream: N/A |
Branch: |
public/17712 |
Dependencies: |
#17711 |
-------------------------+-------------------------------------------------
Comment (by dcoudert):
Hello Nathann,
You are right, we could use a set instead of a dictionary and add the
prefix `P` to the set only if `c(P)<\min_{L\in{\cal L}_P(V)} c(L)`.
However, it is apparently faster to test if a frozenset is a key of a
dictionary than if it is in a set.
{{{
sage: d = dict()
sage: s = set()
sage: for i in range(1, 11):
....: for z in Combinations(range(2*i), i):
....: d[frozenset(z)] = True
....: s.add(frozenset(z))
....:
sage: len(d)
250952
sage: %timeit len(d)
10000000 loops, best of 3: 63 ns per loop
sage: %timeit len(s)
10000000 loops, best of 3: 59.9 ns per loop
sage:
sage: elt = d.keys()[randint(0, len(d)-1)]
sage: %timeit elt in d
10000000 loops, best of 3: 60.9 ns per loop
sage: %timeit elt in s
10000000 loops, best of 3: 163 ns per loop
sage:
sage: elt = d.keys()[randint(0, len(d)-1)]
sage: %timeit elt in d
10000000 loops, best of 3: 58.8 ns per loop
sage: %timeit elt in s
10000000 loops, best of 3: 160 ns per loop
}}}
What we can do is to change `is_known_prefix` as follows:
{{{
if size<1 or size>self.max_prefix_length:
return False
cdef int i
cdef frozenset my_prefix = frozenset([prefix[i] for i in
range(size)])
return my_prefix in self.PT
}}}
and `update` as:
{{{
cdef int i
if size>0 and size<=self.max_prefix_length \
and not (is_improved and cost==upper_bound) \
and len(self.PT)< self.max_prefix_number:
my_prefix = frozenset(prefix[i] for i in range(size))
self.PT[my_prefix] = True
}}}
Furthermore, if we do that inside `BAB_C`, we do only once `my_prefix =
frozenset(prefix[i] for i in range(size))`.
If you agree, I will implement the changes.
David.
--
Ticket URL: <http://trac.sagemath.org/ticket/17712#comment:16>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
