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xkcd #2934: Bloom Filter
(imgs.xkcd.com)
Alt text:
Sometimes, you can tell Bloom filters are the wrong tool for the job, but when they're the right one you can never be sure.
A bloom filter is a data structure that is most useful in creating a spell check algorithm
That's definitely not what they're most useful for. I mean, you probably can use a bloom filter for implementing spell check, but saying that's where they're most useful severely misses the point of probabilistic set membership queries.
Bloom filters and their relatives are great when you have a huge set of values – eg. 100s of millions of user IDs in some database – and you want to have a very fast way of checking whether some value might be in that set, without having to query the database. Naturally this assumes that you've prepopulated a bloom filter with whatever values you need to be checking.
If the result of the bloom filter query is "nope", you know that the value's definitely not in the set, but if the result is "maybe" then you can go ahead and double-check by querying the database. This means that the vast majority of checks don't have to hit that slow DB at all, and even though you'll get some false positives this'll still be much much much faster than having to go through that DB every time.
In this example, what would you use to prepopulate the filter?
Which example do you mean?
If you meant my user ID example, you'd prepopulate the bloom filter with existing user IDs on eg. service startup or whatever, and then update the filter every time a new user ID is added – keeping in mind that the false positive rate will grow as more are added, and that at some point you may need to create a new filter with a bigger backing bit array
So you’re just putting a bunch of values in memory that you can access quickly, like similar to a hash set contains(), maybe hoping for O(1) time. But other than that there’s no trick to it?
Well, yes and no. With a straight-up hash set, you're keeping
set_size * bits_per_elementbits plus whatever the overhead of the hash table is in memory, which might not be tenable for very large sets, but with a Bloom filter that has eg. ~1% false positive rate and an ideal k parameter (number of hash functions, see eg. the Bloom filter wiki article) you're only keeping ~10 bits per element completely regardless of element size because they don't store the elements themselves or even their full hashes – they only tell you whether some element is probably in the set or not, but you can't eg. enumerate the elements in the set. As an example of memory usage, a Bloom filter that has a false positive rate of ~1% for 500 million elements would need 571 MiB (noting that although the size of the filter doesn't grow when you insert elements, the false positive rate goes up once you go past that 500 million element count.)Lookup and insertion time complexity for a Bloom filter is O(k) where k is the parameter I mentioned and a constant – ie. effectively O(1).
Probabilistic set membership queries are mainly useful when you're dealing with ginormous sets of elements that you can't shove into a regular in-memory hash set. A good example in the wiki article is CDN cache filtering: