# Re: [eclipse-clp-users] Computational complexity

From: Alexandre Saidi <Alexandre.Saidi_at_...37...>
Date: Mon, 3 Oct 2011 10:10:14 +0200
```Hi all,
Marco is right.

Furthermore, beside big-O which is the worst case,we're  founded  to ask rather : what is the big-Omega (lower bound) or Theta (almost equality).
I put aside the "average case" which is often harder to compute than the problem itself
Think of Quick-sort which is O(N^2) in the worst case but much less in his average case. Writing Q-sort in CLP/CSP stays O(N^2). The worst case is when the data is already sorted, no matter how you choose the "pivot".

Regards
Alex

Le 30 sept. 2011 à 17:51, Marco Gavanelli a écrit :

> On 30/09/11 14:49, Sergey Dymchenko wrote:
>> Hello!
>>
>> Any hints how to estimate computational complexity (like Big-O
>> notation) of CLP programs? I mean there is no visible cycles, not
>> clear how pruning reduces complexity (does it really reduce in
>> asymptotic sense?) etc...
>
> Hi,
>
> I think it is not clear what you mean exactly.
>
> CLP itself is a superset of Prolog, which is Turing complete, so you can
> write programs of any complexity: it depends on the program you write.
>
> However, CLP is often used to solve CSP problems. CSPs are NP-complete
> problems, so there is no known algorithm less than exponential, so every
> program (including a CLP program) that solves is (nowadays) is exponential.
>
> If you have a CSP with N variables ranging on domains of size D, then
> the search space has size D^N. However, if, thanks to constraint
> propagation, you are able to halve the domains, the search space becomes
> D^N/2^N, so you got an exponential speedup. But depending on the
> problem, you could have no propagation at all, so it really depends on
> the problem you are considering.
>
> Cheers,
> Marco
>
> --
> Marco Gavanelli, Ph.D. in Computer Science
> Dept of Engineering
> University of Ferrara
> Tel/Fax  +39-0532-97-4833
> http://www.ing.unife.it/docenti/MarcoGavanelli/
>
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-------------------------------
Alexandre Saidi
Maitre de Conférences
Ecole Centrale de Lyon-Dép. MI
LIRIS-CNRS UMR 5205
Tél : 0472186530, Fax : 0472186443
```
Received on Mon Oct 03 2011 - 08:08:44 CEST

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