in reply to Re^6: Challenge: Letter Power
in thread Challenge: Letter Power

Since you don't seem to be able to see beyond a pissing contest between my heuristic and my heuristic stuck in a loop, I'll try to make the point another way.

All you are doing at the moment is comparing relative numbers for whichever heuristics you decide to test. And on a miniscule sample of possible datasets. But that gives you no basis upon which to draw any meaningful conclusions.

But in either case, the best solution you have found could be abysmally bad.

So what is the point in being able to say that heuristic A converges on an abysmally bad solution 0.1 seconds more quickly than heuristic B?

For a heuristic to be useful (or even just vaguely meaningful), you have to be able to say something to the effect of: "This heuristic will find the optimal (or one of the top ten most optimal) solution in 90% of cases".

Until you have some way of determining that kind of baseline, comparing trivial modifications of a single heuristic, or two wildly different heuristics, serves little purpose. And you cannot form a baseline without either an exhaustive search or some sound mathematical way of determining or estimating the optimal solution.

If you're really bent on pursuing an algorithm for solving the original problem, then lookup the literature on Linear Programming with particular attention to 'longest path' and 'critical path' analysis in a network. These have known solutions that will guarentee to find an optimal solution faster than a brute force search. Though probably not if coded in Perl.

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.
"Too many [] have been sedated by an oppressive environment of political correctness and risk aversion."

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Re^8: Challenge: Letter Power
by Limbic~Region (Chancellor) on Apr 19, 2009 at 20:57 UTC
    BrowserUk,
    Since you don't seem to be able to see beyond a pissing contest between my heuristic and my heuristic stuck in a loop....

    I am honestly not trying to be thick headed but I do not see what pissing contest you are referring to and for the record, nothing is stuck in a loop. I saw a way to refine your algorithm and asked for your input if you were interested. You could have simply said that you weren't.

    I am sorry that you do not share my appreciation for exploring for exploration's sake but don't tell me there is no value in it. I have certainly learned a lot - something that may even be useful in the practical sense in the future.

    As I have alluded to throughout this thread, I am exploring both heuristic solutions and guaranteed optimal solutions. Since you have made it clear that the only value to you that a heuristic solution has is if you can compare it to the known optimal solution over a large enough data set - I wrote an extremely infantile C brute force implementation that is able to check 3,129,836.24 solutions per second on a single CPU without any compiler optimizations. In other words, it only took 41 minutes to prove the best solution for this data is 446. For me, 41 minutes is still too long so I am exploring other techniques to get under 20 minutes but you weren't interested in that either.

    Your solution, with my refinement, has found the optimal solution within 60 seconds for every random sampling I have been able to do today.

    I won't continue to waste your time since you aren't interested. If you want to see the C (or the perl code to generate it) then feel free to /msg me.

    Update: Adding compiler options gets the C brute force solution to complete all 7,758,767,016 possible solutions in 12 minutes and 24 seconds. I guess I don't need an ingenious solution for that part (10,417,514.7 solutions per second is fast enough for my purposes).

    Cheers - L~R

[reply]
      You could have simply said that you weren't interested.

      I did. Both via /msg, and repeatedly in this thread. And I gave you my reasons why not.

      [the heuristic] has found the optimal solution within 60 seconds for every random sampling
      the C brute force solution to complete all 7,758,767,016 possible solutions in 12 minutes and 24 seconds.

      So what value has the heuristic solution?

      Nobody is going to have a need to solve these puzzles in such large numbers that waiting 15 minutes for the solution is a problem. So being able to say that this heuristic may give you a solution in 60 seconds isn't useful. For a heuristic to be useful there has to be some mathematical basis for believing it can be trusted, as with the Rabin modification of the Miller primality test.

      Had you once in your replies offline or on, indicated that you accepted the need for a reasonable performance brute force mechanism, then I might have been interested in that. As that, as a whole or in parts, could be useful for tackling other, more practical NP hard problems.

      For example, I've a C implementation of the combs() iterator (probably better named arrangements?) from my original post, that cycles through the 7.75e9 arrangements in 45 seconds. (Single threaded). And with suitable pre-encoding of the words, I'm reasonably confident that the scoring of those arrangements shouldn't much more that double that time. If I'm right, and the brute forcing can be achieved in under 2 minutes, what value a sub 60 second maybe?

      With threading, that might be shortened further, and that's something that's right up my alley.

      Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
      "Science is about questioning the status quo. Questioning authority".
      In the absence of evidence, opinion is indistinguishable from prejudice.
[reply]
        BrowserUk,
        I respect you greatly and I consider you a likable person so I apologize for trying your patience. I am not sure why I can't let this go - probably for the same reason I can't let go these interesting distractions. Please keep that in mind as I try and explain my actions - that I am just venting and would be happy to let this drop.

        I did. Both via /msg, and repeatedly in this thread.

        Yes, but you also kept responding even after I said don't feel obliged to indulge me. I misinterpreted this as "I might be interested but you haven't convinced me yet". My apologies.

        So what value has the heuristic solution?

        I too explained my reason, in this thread and through /msg. I learned things I didn't previously know. Techniques that may prove to be useful in the future. I discovered things that didn't work - which by itself is a useful lesson.

        Had you once in your replies offline or on, indicated that you accepted the need for a reasonable performance brute force mechanism

        I mentioned several times in this thread and via /msg that I was also working on a solution that provided a guaranteed optimal solution in a reasonable run time. You didn't inquire further. I agree that I didn't accept that it was necessary. I explained that the heuristic solutions would have personal intrinsic value to me even if I failed in the other task. I still don't think it is necessary but I recognize that if I wanted to gain your interest that is what it would have taken. My apologies and my loss.

        With threading, that might be shortened further, and that's something that's right up my alley.

        Well, I finally posted Challenge: Letter Power Revisited which requires solutions to be pure perl and run in roughly 60 seconds. I know you don't see any value in it but please do share anything you (C, threaded, etc). I would find value in it - I always learn from you.

        Cheers - L~R

[reply]

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