Problems with Hash Tables

http://enfranchisedmind.com/blog/posts/problems-with-hash-tables/

32 30 17 years ago

I've done a search and found that this was submitted a year ago ...

http://news.ycombinator.com/item?id=123718

However, it got no comments, and replies are now closed, so I'll leave this here. Useful information, many lessons to learn. If you're not into algorithms or low level details, you can probably ignore it.

ajross4• 17 years ago

This doesn't make much sense to me. The author correctly identifies that hash resizes that are done by changing the size by a multiple remain O(1) amortized over their construction and use. But then asserts that many hash tables (who?!) don't do this, and that makes them O(N). I've written a ton of hash tables in my career. None have that characteristic. Nor do any I've studied in popular software.

Then he finishes up with a discussion about "bad hash functions" without actually pointing to any examples of tables that use them.

Worst, the point of the whole (rather long!) article is about performance, and yet there's not a benchmark to be seen. Nothing is measured; it's just one assertion after another.

The whole thing is a giant straw man. Not worth reading.

RiderOfGiraffes5• 17 years ago

With respect, I disagree.

It may be that you've never made these mistakes, and you understand all the implications, and you've never had these misconceptions, but of the people with whom I've discussed hash tables, I'd guess that around half have not understood these issues, and have thought that because it's a hash table it's pretty much automatically O(1), and haven't realized that it's amortized.

Not every article about performance needs to include benchmarks to make relevant points. Not every article that talks about implementation details need to give specific examples.

EDIT: FWIW, he does actually give an example of a bad hash function.

In short, I suspect you simply have too much knowledge to find this article useful. That doesn't (necessarily) mean others won't.

So given that you clearly do have a lot of experience in these matters, and given that you say you've written lots of hash-tables in your career, may I ask why? Why not use existing library implementations?

ajross4• 17 years ago

Even if I weren't the best hash author ever (TM), I still wouldn't find much use in this article. You can't argue without evidence, and this provides none. If you want to argue that the amortization creates latency bugs, you need to measure resize latency on some hash or another. If you want to complain about bad hash functions being used, you need to find one and show me a collision rate analysis.

OmniLarry• 17 years ago

"Welcome to amortized analysis!"

Seriously, if the point is to educate people the difference between O(1) and O(1)A, then fine, let people understand the difference. The problem is that he thinks the solution is to scrap it altogether.

It's almost like, hey guys, Quicksort isn't really O(n log n), it only is on average! (Of course, the STD uses introsort.. ;))

joe_the_user3• 17 years ago

Good criticism...

Yet, if you want to avoid your application occasionally freezing when the user hits a key, then isn't distinguishing worst-case scenarios good? You seem to agree with the article's claim that hash table sometimes give you an O(n) hit. Even if this happens very occasionally, aren't there situations where this could be worse than a constant O(log(N)) hit?

On the other, what keeps the hash algorithm from expanding the buckets little-by-little?

ajross4• 17 years ago

Sure, latencies can be a problem. Though even extraordinarily large tables aren't going to have user-visible latencies, really. I'd worry more about real time applications where occasionally high latencies would cause things like buffer underruns. Think packet routers, video transcoders, things like that.

But even then, the naive solution would just be to pre-size the hash table and be careful about insertion/deletion architcture. Not to chuck it in favor of an AVL tree or whatnot.

qhoxie• 17 years ago

That's not the point. I don't think anyone is arguing against what he says about worst case for a well-implemented hash table. The problem is the straw-man: all of the 'bad implementations' he has seen, which is all he really attacks.

tyler• 17 years ago

The part I find particularly silly is where he writes:

  For example, assume that the hash table implementation
  shrinks the table if the number of full buckets drops
  below half, and grows the table if it becomes over full.
  If the table starts out with 100 buckets, and the number 
  of buckets falls to 49, the size is shrunk to 50.

I've never seen a hashtable that actually works this way. It's common knowledge that performance of hashtables degrades long before the "full" point. (I particularly like the explanation of that here: http://eigenclass.org/R2/writings/separate-chaining-vs-doubl...)

barrkel• 17 years ago

However, even if you are using a load factor like .72 or so to decide to grow, such a decision is still sensitive to flip-flopping if you use a very similar boundary for shrinking.

russell• 17 years ago

I think it was a reasonable discussion, it just had some faulty conclusions. Using binary trees for overflow buckets is silly. They may be O(N), but the O can be much larger if you keep them balanced. A much better strategy for dealing with pathological cases is to keep some simple statistics such as the maximum bucket size or the average size of occupied buckets. If you see a pathological case change the hash function and rehash. No need for seeds, or trees or all that.

The discussion of the cost of reallocation seems somewhat overblown. Everyone here knows that if you are going to have a million or billion entries, you dont start with the default allocation or give a fixed increment. Anyway, a good implementation should keep track of the allocation pattern and make adjustments along the way.

He does make a good point that you need to pay attention to your hash function. A good function should try to smear the bits out so that the beginning and end of (say) a string make similar contributions to the hash.

stcredzero2• 17 years ago

The whole thing is a giant straw man. Not worth reading.

His would-be juicy bit about amortized analysis and hash table growth -- this is all freshman undergrad algorithms stuff. Though, it is sad to say, that lots of IT shop pros out there don't know this stuff. (I have been the "guru" or "genius" far too many times, because I know that a naive array add implementation is O(n^2))

nimrody• 17 years ago

Potential benefit of hash tables: cache locality.

Assuming you already have the key in the CPU cache, computing the hash is relatively cheap and gets you directly to the desired value.

A binary tree structure always makes you traverse several levels until you get to the desired value. Of course, this can be minimized with high-fanout trees -- see clojure for example).

rozim• 17 years ago

Cache locality: especially with open addressing and linear probing.

BearOfNH• 17 years ago

Hashtable routines are far easier to write and debug than balanced binary tree routines.

Of course there are open source implementations available for both. But I would guess it is easier to write your own hash function than learn to use somebody else's, and easier to learn somebody else's B-tree routines than to write your own.

So we live in a world with O(N) hash implementations and O(1) B-tree implementations, for N programmers.

antirez• 17 years ago

If you want a compromise that takes little space like hash tables, has average time complexity of O(log(N)) like balanced trees, and is as simple to implement as hash tables, take a look at skip lists.

ggchappell• 17 years ago

The eficiency of hash tables (insertions, in particular), is actually slightly worse than he indicates. They are not amortized O(1) for all data, but only for typical data (or on average over all possible data sets). To see this, suppose that every item inserted happens to go into the same bucket. The amortized time complexity is linear.

On the other hand, insertion is not O(1) even for average data; there is always the periodic table resizing. So: amortized O(1) for average data, not O(1) for average data.

The upshot of all this is that hash tables are still pretty good, but insertion is only constant time in a "double average" sense: on average over a large number of consecutive operations (amortization) and over all possible data sets.

A note to those who say, "Why not just use a different hash function?": This can greatly decrease the probability of poor hash-table performance. But it does not change the worst case, unless we allow for an arbitrarily large number of hash functions, and one of them is guaranteed to be a good one. I've never seen this done (actually, I'm not sure anyone knows how to do it within reasonable efficiency constraints).

And a note to those who say, "But in the real world it doesn't matter": No, sometimes it matters, and sometimes it doesn't. (Don't use Python to program a pacemaker ....)

peterwwillis• 17 years ago

i would love to read this except i am using windows mobile and am shown some "use a different browser!" page instead. this is annoying

blasdel• 17 years ago

He's blocking Opera?

Problems with Hash Tables

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