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### Re: Comparing two arrays

by sundialsvc4 (Abbot)
 on Dec 16, 2013 at 13:05 UTC ( #1067326=note: print w/replies, xml ) Need Help??

in reply to Comparing two arrays

Here’s another way to do it:   scan the arrays to convert them to a vector using some form of “run-length encoding.”   For instance, a list containing the position of the next '1' and the number of '1's that occur.   Now for the magic:   use a Digest algorithm of some sort ... could be CRC, SHA1, could be anything ... to convert that vector into a single value that can be used as a hash.

Actually, if you use a truly-decent message digest algorithm, like SHA1, you probably won’t have to do anything else, because one and only one vector will map to the same hash value.   You have to preprocess each array one time to compute its message-digest hash, but from there on out you might not have to examine the array contents at all.   A comparison of the digests ought to be sufficient.   Aside from the overhead of passing through each array one time to calculate its digest, the overhead of laborious comparison ... disappears.

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Re^2: Comparing two arrays
by roboticus (Chancellor) on Dec 16, 2013 at 13:43 UTC

If you're looking for duplicate vectors, digesting can greatly reduce the number of comparisons, but it won't let you escape them altogether: http://en.wikipedia.org/wiki/Pigeonhole_principle.

Update: s/While/If you're looking for duplicate vectors/ and changed conjunction so the sentence still reads well.

...roboticus

When your only tool is a hammer, all problems look like your thumb.

While digesting can greatly reduce the number of comparisons

That would only be true if the OP was looking for exact matches. He isn't.

He's looking for the best matches, where 'best' is defined in terms of the number of set bits in matching positions. No hashing, digesting nor sorting approach to this problem is possible.

Every X must be fully compared against every Y.

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.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.

That's certainly true, for the original problem. I was intending to refute the statement "because one and only one vector will map to the same hash value", but I didn't take the rest of the thread into context. (I corrected the node accordingly.)

However, you needn't compare each X fully against each Y either, either. Just like your Bloom filter project a while ago, there may be ways to transform the problem so we don't have to explicitly compare vectors against each other. I've been working a bit on one, but I haven't posted it because the performance is currently worse than direct comparisons, and most of the changes I make to it slow it down even further.

...roboticus

When your only tool is a hammer, all problems look like your thumb.

Re^2: Comparing two arrays
by choroba (Bishop) on Dec 16, 2013 at 13:21 UTC
one and only one vector will map to the same hash value
Do you mean there are no hash collisions for SHA1?
لսႽ† ᥲᥒ⚪⟊Ⴙᘓᖇ Ꮅᘓᖇ⎱ Ⴙᥲ𝇋ƙᘓᖇ
Re^2: Comparing two arrays
by BrowserUk (Pope) on Dec 16, 2013 at 15:23 UTC
the overhead of laborious comparison ... disappears.

Total garbage.

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.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.

It is, at best, very rude to say “total garbage” in response to a post ... it doesn’t make you look like a genius, merely a boor.   (I searched the entire thread for the word “best” and did not find it.   Perhaps your eyes are better than mine.)

That being said, i-f the requirement is for “a matching entry,” then the technique that I described will work extremely well.   Strictly speaking, yes, it is possible for (say) a hash-collision to occur, but with a strong algorithm like SHA1 it basically isn’t going to happen.

Any exploitable “predictable fact” about the actual data can be profitably used to reduce the search-space, and (IMHO) in a situation such as this, pragmatically must be.   Even something as basic as “the total number of 1’s” can be pressed into service.   If you can “reasonably predict” that the differences between the searched-for array and the “best fit” that will be found will consist, let’s say, of a change-of-state of no more than (some) n positions, then even a brute-force search could be limited to consider only the candidates which fall into that range, perhaps starting with any exact-matches and then working outward ± x for x in (1..n).   This does, of course, open up the possibility of a statistical Type-2 Error (concluding that no best-match exists when in fact one does), but this might be judged to be either acceptable or necessary.   (Or not ...)

If necessity really must become the mother of invention, and once again if you know that there are exploitable characteristics of the data, it is also possible to apply hashing or ones-counting to slices of the total vector.   Instead of merely counting all the 1’s, count them in every (say) thousand bits.   Apply some useful heuristic to this vector of sums to decide whether you choose to examine the whole thing.

In the end, the problem won’t be completely-abstract, nor will be its solution.   There must be something, in the real world, that stipulates what is and what is not “best,” or even “plausible.”   It’s my opinion that you must solve this problem, at least in significant part, by reducing the total number of vectors that you consider, and by selecting for consideration only those which are “most likely.”   Representational optimizations such as the use of bit-vectors may also be important, but even these can’t be applied in a brute-force way.   You’ll simply never get the work done.

Re^2: Comparing two arrays
by GotToBTru (Prior) on Dec 31, 2013 at 21:38 UTC

This method was considered and discarded in the OP:

I was thinking about computing a hash key (a checksum of come sort) but then i would be able to identify only identical (x,y) pairs.

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