#8227: Improving iterated palindromic closure computation
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Reporter: abmasse | Owner: abmasse
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.3.3
Component: combinatorics | Keywords: iterated palindromic closure
Author: abmasse | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Description changed by abmasse:
Old description:
> There is a faster way to compute the iterated paindromic closure of a
> word than using the definition. The problem with the latter is that it
> needs to compute the longest f-palindromic suffix of the current word at
> each step, while it is possible to easily deduce this length only by
> looking at the directive word.[[BR]]
> Here is an example:
> {{{
> sage: w = words.RandomWord(10)
> sage: w.iterated_right_palindromic_closure(algorithm='definition')
> word: 0010010001001000100100010010001001001000...
> sage: timeit("print
> w.iterated_right_palindromic_closure(algorithm='definition').length()")
> 5 loops, best of 3: 211 ms per loop
> sage: timeit("print
> w.iterated_right_palindromic_closure(algorithm='recursive').length()")
> 25 loops, best of 3: 9.46 ms per loop
> }}}
> The difference is particularly notable for longer words:
> {{{
> sage: w = words.RandomWord(15)
> sage: timeit("print
> w.iterated_right_palindromic_closure(algorithm='definition').length()")
> 5 loops, best of 3: 3.73 s per loop
> sage: timeit("print
> w.iterated_right_palindromic_closure(algorithm='recursive').length()")
> 25 loops, best of 3: 37.4 ms per loop
> }}}
New description:
There is a faster way to compute the iterated palindromic closure of a
word than using the definition. The problem with the latter is that it
needs to compute the longest f-palindromic suffix of the current word at
each step, while it is possible to easily deduce this length only by
looking at the directive word.[[BR]]
Here is an example:
{{{
sage: w = words.RandomWord(10)
sage: w.iterated_right_palindromic_closure(algorithm='definition')
word: 0010010001001000100100010010001001001000...
sage: timeit("print
w.iterated_right_palindromic_closure(algorithm='definition').length()")
5 loops, best of 3: 211 ms per loop
sage: timeit("print
w.iterated_right_palindromic_closure(algorithm='recursive').length()")
25 loops, best of 3: 9.46 ms per loop
}}}
The difference is particularly notable for longer words:
{{{
sage: w = words.RandomWord(15)
sage: timeit("print
w.iterated_right_palindromic_closure(algorithm='definition').length()")
5 loops, best of 3: 3.73 s per loop
sage: timeit("print
w.iterated_right_palindromic_closure(algorithm='recursive').length()")
25 loops, best of 3: 37.4 ms per loop
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8227#comment:6>
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