You want a structure that can tell you something has been seen, but sometimes forgets, but will never incorrectly tell you something has been seen.

Solution: an array. Hash the item to find its index, swap out what's there, and see if it is your item. If so, you know for sure it was previously placed. If not, then it might not have (it may have been forgotten).

  let arr = Array of key
  let contains_key key = 
    let index = hash key % arr.length
    let prev_key = arr.swap[index, key]
    return prev_key = key

On that subject, you might as well have an LRU valueless cache if locality is going to play a role.

Don't think you meant that.

Relatedly, the majority(?) of audio processing is just creative use of buffers.

          | P | M | N
    Bloom | X | X |
    Oppos | X |   |

True, although the probability of a false answer given that we combine them can be smaller from the probability of the same false answer in the case when we use each of them separately. This may be important in cases when the aversion to false answers is extremely high.

So, could also consider adding probing to lessen destructive collisions (up to some chosen probing depth) while there are other unused slots, in still-constant average time. Or, any other choice-of-slots approach such as 'cuckoo hashing':

http://en.wikipedia.org/wiki/Hash_table#Cuckoo_hashing

Whether you'd want to pay that cost could depend on how soon you reach saturation within each reset period, after which 'every' insert results in an eviction. But if you were usually in one-for-one eviction mode, you might add a bit or more that hints 'age' or 'recent access' to probed items. Then each eviction could be biased towards an older/less-accessed value... taking more advantage of the clustering-in-time that was reported.

And once you add that aging bit you might not need discrete full-restart periods ("hourly") at all: just make a useful proportion of older entries eligible for eviction each interval, maintaining a steady-state of full-array, evictions-biased-towards-older-entries.

A structure that may report false positives, but no false negatives: A single bit set to 1

A structure that may report false negatives, but no false positives: A single bit set to 0

Obviously that's entirely useless, but I think it shows that you can't make any definitive proof of size requirements

You have to define more specifically what you mean about accuracy here. Accuracy for the bloom filter would be probability of false positives. For the inverse it would be probability of false negatives.

For a bloom filter, if you're targeting a false probability f with n items, you want k = lg(1)/f hash functions, and m = 1.44 k*n bits.

That's the thing though. The bloom filter version scales up easily from the degenerate version (adding more bits increases accuracy). Unless I'm missing something, the inverse bloom filter doesn't scale up from the degenerate version in any natural way.

This will nag at me now. I'm going to need to give this some thought. If I come up with any proof on mem reqs. I'll let you know.

I use bloom filters in an application at work and was very interested to hear about this, wondering if some sort of hybrid might be useful. But when I saw that the hash map was storing the actual objects, I immediately dismissed the idea for my use case - we can't afford to store anything more than a handful of bits. (Our bloom filters set between 9 and 11 bits per signature.)

The key advantage to bloom filters is that the represent set identity lookups (albeit in an adjustable lossy false-positive way). They do not, however, store actual sets of data. They must be coupled with a storage mechanism (traditionally with a several-order-of-magnitude slower lookup speed than the bloom filter) to actually store the items contained within the set - the bloom filter is just a way of definitively answering the question "Could this set possibly contain this item?"

Also, if memory is actually an issue, he should store hashes instead of full objects (assuming the byte arrays are more than 16 bytes).

But, since the hash table is not going to grow in this particular case, any perf gain from using a power of 2 will probably be far less important.

1. If you're using a non-trivial hash function, one more modulo calculation at the end to get the actual memory address is not a big difference.

2. If you're using a trivial hash function, I bet for a lot of data sets you'll get fewer collisions with a hash table whose size is a prime number, canceling out any benefit from calculating the address slightly faster.

  >>> my_dict = {}
  >>> my_dict[item] = True #Insert an item
  >>> try:
  ...    tmp = my_dict[item]
  ...    print "Found"
  ... except KeyError:
  ...    print "Not found"

You can add code to get around that (e.g. expiration times), but it also might be easier (and have less memory usage) to write your own dict class that overwrites values when a collision occurs.

Also, since the OP seems to be using java: if you can get away with storing a primitive data type in an array (e.g. array of int or long) you can save a lot of memory vs using a Set or Map.

Also, in your example you're storing True as the value, but if you do that, you can't tell the difference between rbloom_array[hashfunc(item1)] and rbloom_array[hashfunc(item2)], if hashfunc(item1) == hashfunc(item2) (that is, they collide). You'd need to store the actual item in the data structure, not just a bit, and then you compare what you get out of the data structure to what you're trying to put in it. If the _items_ are equal then it's a duplicate and you can skip the write (to the database, from the example). If the items are not equal, you need to do the write.

If the bloom filter says 'yes I've seen it!', and the opposite filter says 'nope, not here', which is accurate? You know it's either a false-positive from the bloom filter or it a false-negative from the opposite filter, but that's the limit of your information. Effectively, you've partitioned your set into three: [definitely not, ambiguous, definitely seen].

If you want to know 100% of the items you've stored with full fidelity, you need to store information for all of them (e.g. in a hash table). Which is a valid thing to do, but requires a lot more memory than the author of this article was willing to use.

In the case of your specific suggestion, though, the problem is this: what if the bloom filter says "I've seen it (but could be lying)", and the "opposite" filter says "I've never seen it (but could be lying)"? Then you still have no idea whether the object is in the set.

Unless there are regularities in the data that you can exploit.

It's correct to say that the bloom filter will produce no false negatives and the OOABF will produce no false positives, so if your OOABF returns true or your bloom filter returns false then you know for sure whether you've seen the item before. The trouble happens when your OOABF returns false and your bloom filter returns true, in which case you might have seen it before.

A good way to look at the problem is that you have N keys to store (because you cannot have false positives). So with N keys, if you want less than sizeof(N)*N bytes, the only real answer is compression. So either you just discard data (what the OP does), or find a clever way to compress things.

The benefit is that you're only testing for existence, so that gives you some leeway. For instance, suppose you are getting random 8-byte user IDs. You could store, say, 1M of them in a hashtable, then take those items, sort them, and store deltas. Instead of 8 bytes per item, you'd only need 44 bits on average (2^64/1M) to store the differences. I believe this is what the OP suggested at the end of the article.

So, it really depends on the key types, and the penalty for forgetting an item. At a really high penalty (say, something that needs to perform an ACID SQL transaction), maintaining a compressed block of IDs is rather attractive. Whereas, if it's just sending an extra write to a high-perf write store, maybe it doesn't matter, and the OPs quick forgetful array is useful.

The description in this article seems to add too much complexity ("the opposite of a bloom filter") for what really is just a simple cache (albeit, IMO, a relatively inefficient one for the problem he describes).

A ConcurrentLinkedHashMap (http://code.google.com/p/concurrentlinkedhashmap/) solved it easily. It does use more RAM though... but an insignificant amount on our heap.

True positive is when all places for given entry contain 1.

Adding is incrementing all places (if they have value less than 2).

Before putting new value in check if it's not already here. If it is don't add.

  perl -MDigest::MD5 -nle '($id,@data)=split;$t=time;$j=unpack("L", Digest::MD5::md5($id))%100;print join(" ",$id,@data) if $t-$h{$j}>3600 or $hi{$j} ne $id;$h{$j}=$t;$hi{$j}=$id' input

When there is a collision you check to see if the object living there is the one you're trying to store. If it's not then you assume negative. If it is the object you're checking then it's positive but it's a correct positive.

If it's not the object you're checking then you evict the object living there and put in the one you're checking, thus allowing the one you evicted to cause a false negative again.

The whole system works BECAUSE of intentional collisions. If there were no collisions it would just be a hashmap and you'd have unbounded data structure size.

With a bloom filter, you can take gigabyte-sized video files and determine if they have never been seen by the bloom filter. And the size of the bloom filter is fixed; choose the size based on expected inputs, desired accuracy, and so on and it doesn't grow based on the size of the objects being processed. With this implementation, it stores not only the hash of the video but the entire byte array of the video at the hash location in order to not have a false positive.

So it's possible to have an opposite-of-a-bloom-filter with only 8 buckets, but it consumes terabytes of storage space because you're processing really massive files.