Re^4: Out of Memory when generating large matrix (space complexity)
by LanX (Bishop) on Mar 07, 2018 at 01:31 UTC

> but there is also Counting Sort, Radix Sort, and other forms of distribution sorting that are of high utility in realworld applications.
These algorithms are all limited to elements of fixed length (which is the case), but Sundial suggested unix sort which knows nothing about the nature of the input.
And did you try to look into the space complexity of your suggestions?
Counting Sort requires 4**21 buckets. Seriously ???
Radix Sort is still the best in this respect, but has O(l*n) with l length of alphabet (here 21).
Even worse identical elements are in worst case only identified in the last step, requiring to be able to hold all elements in memory, while shifting them all l times from bucket to bucket.
A hash count can go thru different files without keeping them all in memory, because identical elements collapse into one count.
Last but not least, a hash count is much easier implemented.
Cheers Rolf
_{(addicted to the Perl Programming Language and ☆☆☆☆ :)
Wikisyntax for the Monastery
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 [reply] 

Well, I glanced "(space complexity)" in the title and thought there is a glimmer of hope for you, yet.
You have identified the problem area, but again deftly avoid seeing the light. Sorting (or deduplicating) is a problem with O(n log n) time complexity. If you have a hash function that successfully distributes the keys, you can cut down the problem and move some of the complexity into space domain.
Hashes are O(n) both in time and space complexity (list insertion). Streaming merge is O(1) in space complexity. Partial hashing is possible. Using a hash table of size k, you can modify the algorithm to achieve O(n log(n/k)) in time complexity, and O(k) in space complexity. The k scales well until you break out of the CPU caches, after which it scales rather poorly. I referenced another thread where someone run into a brick wall trying to hash just 36M elements. Sortuniq proved to be greatly superior in that case.
So far, you have
 veered the topic into discussion of algorithmic complexity, where noone really asked for it.
 misapplied the big O notation. Big O does not say whether one solution is faster than other. It tells you about how a problem scales.
 made the incorrect statement that a hash based solution would scale better than merge sort. In practice, hashing does not scale beyond memory limits.
 made some ludicrously inappropriate suggestion of using wc; this suggests you did not invest the cycles necessary to understand the problem, let alone offer a solution.
 applied some technique (hashing) as a magic bullet, without the fundamental grasp of subject matter. This is Cargo Cult by definition.
By the way, I never argued that a hash count was unsuitable. By all means, ++$count{$key} if that works. But you chose to attack a broken clock, and forgot that a broken clock, too, is right two times a day.
 [reply] [d/l] 

> glimmer of hope for you,
Wow, you are so humble and your posts so clear and understandable.
No wonder you prefer to post anonymously.
(closed :)
Cheers Rolf
_{(addicted to the Perl Programming Language and ☆☆☆☆ :)
Wikisyntax for the Monastery
}
 [reply] 
Re^4: Out of Memory when generating large matrix
by LanX (Bishop) on Mar 06, 2018 at 13:26 UTC

> Generic sort is O(n log n), but there is
The best generic sorts are O(n log n) (worst case matters), SD was seemingly talking about the command line utility sort , which is generic .
> It is important to understand that hashing is not algorithmically superior to sorting, indeed it is a specific form of sorting in disguise.
I disagree because as I already said counting by hashing is one pass and is loosing any order information.
Sort is about ordering and I don't see a way to make this in one pass.
But I'd be interested to see your evidence about how the information loss from hashing can be compensated ...
Cheers Rolf
_{(addicted to the Perl Programming Language and ☆☆☆☆ :)
Wikisyntax for the Monastery
}
 [reply] [d/l] 
Re^4: Out of Memory when generating large matrix
by BrowserUk (Pope) on Mar 06, 2018 at 15:42 UTC

 [reply] 

Hashing in a nutshell: apply hash function f() to the keys, bucket the data records accordingly. Where a radix sort would use part of the key directly (like a hash function that just masks bits), hashing picks a more complicated function. So there's a tradeoff. Your data is no longer sorted by the key, but by f(key). On the other hand, you get a flat distribution that makes the bucketing work.
Can you truly not see the similarity between distribution sort and hashing?
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Once you move outside of academia and thesis, it isn't the algorithm, but the implementation that is important. A mergesort programmed badly can be much slower than a bubble sort done well.
And once you recognise that in the real world, implementation is king, any kind of disk based sort is glacial compared to a memorybased hash.
It isn't the similarities, but the differences that are important.
A stately home and a plane both have wings, windows and seats, but the differences outweigh those similarities for most practical considerations.
With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
Examine what is said, not who speaks  Silence betokens consent  Love the truth but pardon error.
In the absence of evidence, opinion is indistinguishable from prejudice.
Suck that fhit
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Re^4: Out of Memory when generating large matrix
by LanX (Bishop) on Mar 06, 2018 at 13:42 UTC

> counting unique elements
What is that supposed to mean?
The elements are by definition unique IFF their count is one!
Cheers Rolf
_{(addicted to the Perl Programming Language and ☆☆☆☆ :)
Wikisyntax for the Monastery
}
 [reply] 

It was supposed to mean that a count is obtained for each of the (unique) element in a set. (Not the number of unique elements.) It doesn't really matter though, what is important is that a set on unique elements has to be constructed.
Constructing a set of unique elements is the same (algorithmically) as sorting, with the proviso that an ordered comparison function is available (i.e. set can be ordered). If only compare for equality is available, the construction becomes O(n*n).
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SD, this doesn't make sense.
Cheers Rolf
_{(addicted to the Perl Programming Language and ☆☆☆☆ :)
Wikisyntax for the Monastery
}
 [reply] 