I have a set of C++ functions. I want to map this functions in an hash table, something like: unordered_map<function<ReturnType (Args...)> , SomethingElse>, where SomethingElse is not relevant for this question.
This set of functions is previously known, small (let say less than 50) and static (is not gonna change).
Since lookup performance is crucial (should be performed in O(1)), I want to define a perfect hashing function.
There exists a perfect hash function generator for this scenario?
I know that there exists perfect hashing functions generators (like GPERF or CMPH) but since I've never used them, I don't know if they're suitable for my case.
REASON:
I'm trying to design a framework where, given a program written in C++, the user can select a subset F of the functions defined in this program.
For each f belonging to F, the framework implements a memoization strategy: when we call f with input i, we store (i,o) inside some data structure. So, if we are going to call AGAIN f with i, we will return o without performing again the (time expensive) computation.
The "already computed results" will be shared among different users (maybe on the cloud), so if user u1 has already computed o, user u2 will save computing time calling f with i (using the same annotation of before).
Obviously, we need to store the set of pairs (f,inputs_sets) (where inputs_sets is the already computed results set that I talked before), which is the original question: how do I do it?
So, using the "enumeration trick" proposed in the comments in this scenario could be a solution, assuming that the all the users use the exactly same enumeration, which could be a problem: supposing that our program has f1,f2,f3 what if u1 wants to memoize only f1 and f2 (so F={f1,f2}), while u2 wants to memoize only f3 (so F={f3})? An overkill solution could be to enumerate all the functions defined in the program, but this could generate an huge waste of memory.
Ok, maybe not what you want to hear but consider this: since you talk about a few functions, less than 50, the hash lookup should be negligible, even with collisions. Have you actually profiled and saw that the lookup is critical?
So my advise is to focus your energy on something else, most likely a perfect hash function would not bring any kind of improved performance in your case.
I am going to go one step further and say that I think that for less than 50 elements a flat map (good ol' vector) would have similar performance (or maybe even better due to cache locality). But again, measurements are required.
Related
I'm trying to create a general memoizator for multiple and arbitrary functions.
For each function std::function<ReturnType(Args...)> that we want to memoize, we unordered_map<Args ..., ReturnType> (I'm keeping things simple on purpose).
The big problem comes when our memoized function has some really big argument Args ...: for example let suppose that our function sort a vector of 10 millions numbers and then returns the sorted vector, so something like std::function<vector<double>(vector<double>)>.
As you can imagine, after having inserted less than 100 vectors, we have already filled 8 GBS of memory. Notice that maybe this is given from the combination of huge vectors and the memory required by the sorting algorithm (I didn't investigate on the causes).
So what about if instead of the structure described above, we define unordered_map<UUID(Args ...), ReturnType> (where UUID= Universally Unique Identifier)? We should relax the deterministic feature (so maybe we return a wrong error), but with a very low probability.
The problem is that since I never used UUIDs, I don't know if there are suitable implementations for this application.
So my question is:
There exists a better solution than UUIDs for this problem?
Which UUID implementation is better suitable for this problem?
boost uuid is a possible candidate?
Unfortunately, the problem could be solved for Args ... but not for ReturnType, so there is a solution for memoized result?
Notice that the UUIDs generated for the object x should be the same even in different runs and machines.
Notice that if we have the same UUID for two different objects (and so we return the wrong value) with a really low probability, then it could be acceptable...let's say that this could be a "probabilistic memoizator".
I know that this application doesn't make sense in a memoization context (what are the odds that an user asks two times to sort the same 10 millions elements vector?), but it's time and memory expensive (so good for benchmarking and to introduce the memory problem that I stated above), so please don't whip and crucify me because this is an absurd memoization application.
Identifying any object is easy. The address is "object identity" in C++. This is also the reason that even empty classes cannot have zero size.
Now, what you want is value equivalence. That's strictly not in the language domain. It's solidly in the application/library logic domain.
You should consider using something like boost::flyweights. It has precisely this facility, and makes it "easy" to customize the equivalence semantics for your types.
I am new to the hashing in general and also to the STL world and saw the new std::unrdered_set and the SGI :hash_set,both of which uses the hasher hash. I understand to get a good load factor , you might need to write your own hashfunction, and I have been able to write one.
However, I am trying to go deep into , how the original default has_functions are written.
My question is :
1) How is the original default HashFcn written ; more concretely how is the hash generated?
Is it based on some pseudo random number. Can anyone point me to some header file (I am a bit lost with the documentation), where I can look up ; how the hasher hash is implemented.
2)How does it guarantee that each time , you will be able to get the same key?
Please, let me know if I can make my questions clearer any way?
In the version of gcc that I happen to have installed here, the required hash functions are in /usr/lib/gcc/i686-pc-cygwin/4.7.3/include/c++/bits/functional_hash.h
The hashers for integer types are defined using the macro _Cxx_hashtable_define_trivial_hash. As you might expect from the name, this just casts the input value to size_t.
This is how gcc does it. If you're using gcc then you should have a similarly-named file somewhere. If you're using a different compiler then the source will be somewhere else. It is not required that every implementation uses a trivial hash for integer types, but I suspect that it is very common.
It's not based on a random number generator, and hopefully it's now pretty obvious to you how this function guarantees to return the same key for the same input every time! The reason for using a trivial hash is that it's as fast as it gets. If it gives a bad distribution for your data (because your values tend to collide modulo the number of buckets) then you can either use a different, slower hash function or a different number of buckets (std::unordered_set doesn't let you specify the exact number of buckets, but it does let you set a minimum). Since library implementers don't know anything about your data, I think they will tend not to introduce slower hash functions as the default.
A hash function must be deterministic -- i.e., the same input must always produce the same result.
Generally speaking, you want the hash function to produce all outputs with about equal probability for arbitrary inputs (but while desirable, this is no mandatory -- and for any given hash function, there will always be an arbitrary number of inputs that produce identical outputs).
Generally speaking, you want the hashing function to be fast, and to depend (to at least some degree) on the entirety of the input.
A fairly frequently seen pattern is: start with some semi-random input. Combine one byte of input with the current value. Do something that will move the bits around (multiplication, rotation, etc.) Repeat for all bytes of the input.
A generally asked question is whether we should use unordered_map or map for faster access.
The most common( rather age old ) answer to this question is:
If you want direct access to single elements, use unordered_map but if you want to iterate over elements(most likely in a sorted way) use map.
Shouldn't we consider the data type of key while making such a choice?
As hash algorithm for one dataType(say int) may be more collision prone than other(say string).
If that is the case( the hash algorithm is quite collision prone ), then I would probably use map even for direct access as in that case the O(1) constant time(probably averaged over large no. of inputs) for unordered_map map be more than lg(N) even for fairly large value of N.
You raise a good point... but you are focusing on the wrong part.
The problem is not the type of the key, per se, but on the hash function that is used to derive a hash value for that key.
Lexicographical ordering is easy: if you tell me you want to order a structure according to its 3 fields (and they already support ordering themselves) then I'll just write:
bool operator<(Struct const& left, Struct const& right) {
return boost::tie(left._1, left._2, left._3)
< boost::tie(right._1, right._2, right._3);
}
And I am done!
However writing a hash function is difficult. You need some knowledge about the distribution of your data (statistics), you might need to prevent specially crafted attacks, etc... Honestly, I do not expect many people of being able to craft a good hash function. But the worst part is, composition is difficult too! Given two independent fields, combining their hash value right is hard (hint: boost::hash_combine).
So, indeed, if you have no idea what you are doing and you are treating user-crafted data, just stick to a map. It's maybe slower (not sure), but it's safer.
There isn't really such a thing as collision prone object, because this thing is dependent on the hash function you use. Assuming the objects are not identical - there is some feature that can be utilized to create an informative hash function to be used.
Assuming you have some knowledge on your data - and you know it is likely to have a lot of collision for some hash function h1() - then you should find and use a different hash function h2() which is better suited for this task.
That said, there are other issues as well why to favor tree based data structures over hash bases (such as latency and the size of the set), some are covered by my answer in this thread.
There's no point trying to be too clever about this. As always, profile, compare, optimise if useful. There are many factors involved - quite a few of which aren't specified in the Standard and will vary across compilers. Some things may profile better or worse on specific hardware. If you are interested in this stuff (or paid to pretend to be) you should learn about these things a bit more systematically. You might start with learning a bit about actual hash functions and their characteristics. It's extremely rare to be unable to find a hash function that has - for all practical purposes - no more collision proneness than a random but repeatable value - it's just that sometimes it's slower to approach that point than it is to handle a few extra collisions.
Is there a way to write simple hashtable with the key as "strings" and value as the frequency, so that there are NO collisons? There will no be removal from the hashtable, and if the object already exists in the hashtable, then just update its frequency(add them together).
I was thinking there might be a algorithm that can compute a unique number from the string which will be used as the index.
Yes, i am avoiding the use of all STL construct including unordered_map.
You can use any perfect hash generator like gperf
See here for a list: http://en.wikipedia.org/wiki/Perfect_hash_function
PS. You'd still possibly want to use a map instead of flat array/vector in case the mapped domain gets too big/sparse
It really depends on what you mean by 'simple'.
The std::map is a fairly simple class. Still, it uses a red-black tree with all of the insertion, deletion, and balancing nicely hidden away, and it is templated to handle any orderable type as a key and any type as the value. Most map classes use a similar implementation, and avoid any sort of hashing functionality.
Hashing without collisions is not a trivial matter whatsoever. Perhaps the simplest method is Pearson Hashing.
It seems like you have 3 choices:
Implement your own perfect hashing class. This would be a pretty good sized class with a lot of functionality and some decently complex algorithms. I don't think this is simple.
Download and use a perfect hashing library that is already out there. Of course, you have to worry about deployability.
Use STL's map class. It's embedded, well-documented, easy to use, type-flexible, and completely cross-platform. This seems like the 'simplest' solution.
If I may ask, Why are you avoiding STL?
If the set of possible strings is known beforehand, you can use a perfect hash function generator to do this. But otherwise, what you ask is impossible.
Now, it IS possible to make the likelihood of collisions extremely low by using a good hash function and making sure your table is huge. You basically need a big enough table to make the likelihood of invoking the Birthday Paradox low enough to suit you. Then you just use n bits of output from SHA-1, and 2^n will be your table size.
I'm also wondering if maybe you could use a Bloom filter and have an actual counter instead of bits. Keep a list of all the words you've stuffed into the bloom filter and what entries they've incremented (which will be the same each time) and you have yourself a gigantic linear function that you might be able to solve to get all the individual counts back out again.
In one of the applications I work on, it is necessary to have a function like this:
bool IsInList(int iTest)
{
//Return if iTest appears in a set of numbers.
}
The number list is known at app load up (But are not always the same between two instances of the same application) and will not change (or added to) throughout the whole of the program. The integers themselves maybe large and have a large range so it is not efficient to have a vector<bool>. Performance is a issue as the function sits in a hot spot. I have heard about Perfect hashing but could not find out any good advice. Any pointers would be helpful. Thanks.
p.s. I'd ideally like if the solution isn't a third party library because I can't use them here. Something simple enough to be understood and manually implemented would be great if it were possible.
I would suggest using Bloom Filters in conjunction with a simple std::map.
Unfortunately the bloom filter is not part of the standard library, so you'll have to implement it yourself. However it turns out to be quite a simple structure!
A Bloom Filter is a data structure that is specialized in the question: Is this element part of the set, but does so with an incredibly tight memory requirement, and quite fast too.
The slight catch is that the answer is... special: Is this element part of the set ?
No
Maybe (with a given probability depending on the properties of the Bloom Filter)
This looks strange until you look at the implementation, and it may require some tuning (there are several properties) to lower the probability but...
What is really interesting for you, is that for all the cases it answers No, you have the guarantee that it isn't part of the set.
As such a Bloom Filter is ideal as a doorman for a Binary Tree or a Hash Map. Carefully tuned it will only let very few false positive pass. For example, gcc uses one.
What comes to my mind is gperf. However, it is based in strings and not in numbers. However, part of the calculation can be tweaked to use numbers as input for the hash generator.
integers, strings, doesn't matter
http://videolectures.net/mit6046jf05_leiserson_lec08/
After the intro, at 49:38, you'll learn how to do this. The Dot Product hash function is demonstrated since it has an elegant proof. Most hash functions are like voodoo black magic. Don't waste time here, find something that is FAST for your datatype and that offers some adjustable SEED for hashing. A good combo there is better than the alternative of growing the hash table.
#54:30 The Prof. draws picture of a standard way of doing perfect hash. The perfect minimal hash is beyond this lecture. (good luck!)
It really all depends on what you mod by.
Keep in mind, the analysis he shows can be further optimized by knowing the hardware you are running on.
The std::map you get very good performance in 99.9% scenarios. If your hot spot has the same iTest(s) multiple times, combine the map result with a temporary hash cache.
Int is one of the datatypes where it is possible to just do:
bool hash[UINT_MAX]; // stackoverflow ;)
And fill it up. If you don't care about negative numbers, then it's twice as easy.
A perfect hash function maps a set of inputs onto the integers with no collisions. Given that your input is a set of integers, the values themselves are a perfect hash function. That really has nothing to do with the problem at hand.
The most obvious and easy to implement solution for testing existence would be a sorted list or balanced binary tree. Then you could decide existence in log(N) time. I doubt it'll get much better than that.
For this problem I would use a binary search, assuming it's possible to keep the list of numbers sorted.
Wikipedia has example implementations that should be simple enough to translate to C++.
It's not necessary or practical to aim for mapping N distinct randomly dispersed integers to N contiguous buckets - i.e. a perfect minimal hash - the important thing is to identify an acceptable ratio. To do this at run-time, you can start by configuring a worst-acceptible ratio (say 1 to 20) and a no-point-being-better-than-this-ratio (say 1 to 4), then randomly vary (e.g. changing prime numbers used) a fast-to-calculate hash algorithm to see how easily you can meet increasingly difficult ratios. For worst-acceptible you don't time out, or you fall back on something slower but reliable (container or displacement lists to resolve collisions). Then, allow a second or ten (configurable) for each X% better until you can't succeed at that ratio or reach the no-pint-being-better ratio....
Just so everyone's clear, this works for inputs only known at run time with no useful patterns known beforehand, which is why different hash functions have to be trialed or actively derived at run time. It is not acceptible to simple say "integer inputs form a hash", because there are collisions when %-ed into any sane array size. But, you don't need to aim for a perfectly packed array either. Remember too that you can have a sparse array of pointers to a packed array, so there's little memory wasted for large objects.
Original Question
After working with it for a while, I came up with a number of hash functions that seemed to work reasonably well on strings, resulting in a unique - perfect hashing.
Let's say the values ranged from L to H in the array. This yields a Range R = H - L + 1.
Generally it was pretty big.
I then applied the modulus operator from H down to L + 1, looking for a mapping that keeps them unique, but has a smaller range.
In you case you are using integers. Technically, they are already hashed, but the range is large.
It may be that you can get what you want, simply by applying the modulus operator.
It may be that you need to put a hash function in front of it first.
It also may be that you can't find a perfect hash for it, in which case your container class should have a fall back position.... binary search, or map or something like that, so that
you can guarantee that the container will work in all cases.
A trie or perhaps a van Emde Boas tree might be a better bet for creating a space efficient set of integers with lookup time bring constant against the number of objects in the data structure, assuming that even std::bitset would be too large.