I need to implement a fixed-size hash map optimized for memory and speed, but am unclear as to what this means: Does it mean that the number of buckets I can have in my hash map is fixed? Or that I cannot dynamically allocate memory and expand the size of my hash map to resolve collisions via linked lists? If the answer to the latter question is yes, the first collision resolution approach that comes to mind is linear probing--can anyone comment on other more memory and speed efficient methods, or point me towards any resources to get started? Thanks!
Without seeing specific requirements it's hard to interpret the meaning of "fixed-size hash map optimized for memory and speed," so I'll focus on the "optimized for memory and speed" aspect.
Memory
Memory efficiency is hard to give advice for particularly if the hash map actually exists as a "fixed" size. In general open-addressing can be more memory efficient because the key and value alone can be stored without needing pointers to next and/or previous linked list nodes. If your hash map is allowed to resize, you'll want to pick a collision resolution strategy that allows for a larger load (elements/capacity) before resizing. 1/2 is a common load used by many hash map implementations, but it means at least 2x the necessary memory is always used. The collision resolution strategy generally needs to be balanced between speed and memory efficiency, in particular tuned for your actual requirements/use case.
Speed
From a real-world perspective, particularly for smaller hash-maps or those with trivially sized key, the most important aspect to optimizing speed would likely be reducing cache-misses. That means put as much of the information needed to perform operations in contiguous memory spaces as possible.
My advice would be to use open-addressing instead of chaining for collision resolution. This would allow for more of your memory to be contiguous and should be at a minimum 1 less cache miss per key comparison. Open-addressing will require some-kind of probing, but compared to the cost of fetching each link of a linked list from memory looping over several array elements checking key comparison should be faster. See here for a benchmark of c++ std::vector vs std::list, the takeaway being for most operations a normal contiguous array is faster due to spatial locality despite algorithm complexity.
In terms of types of probing, linear probing has an issue of clustering. As collisions occur the adjacent elements are consumed which causes more and more collisions in the same section of the array, this becomes exceptionally important when the table is nearly full. This could be solved with re-hashing, Robin-Hood hashing (As you are probing to insert, if you reach an element closer to it's ideal slot than the element being inserted, swap the two and try to insert that element instead, A much better description can be seen here), etc. Quadratic Probing doesn't have the same problem of clustering that linear probing has, but it has it's own limitation, not every array location can be reached from every other array location, so dependent on size, typically only half the array can be filled before it would need to be resized.
The size of the array is also something that effects performance. The most common sizings are power of 2 sizes, and prime number sizes. Java: A "prime" number or a "power of two" as HashMap size?
Arguments exist for both, but mostly performance will depend on usage, specifically power of two sizes are usually very bad with hashes that are sequential, but the conversion of hash to array index can be done with a single and operation vs a comparatively expensive mod.
Notably, the google_dense_hash is a very good hash map, easily outperforming the c++ standard library variation in almost every use case, and uses open-addressing, a power of 2 resizing convention, and quadratic probing. Malte Skarupke wrote an excellent hash table beating the google_dense_hash in many cases, including lookup. His implementation uses robin hood hashing and linear probing, with a probe length limit. It's very well described in a blog post along with excellent benchmarking against other hash tables and a description of the performance gains.
Related
As I have studied HashSet class, it uses the concept of filled ratio, which says if the HashSet if filled up to this limit create a larger HashSet and copy values in to it. Why we dont let HashSet to get full with object and then create a new HashSet? Why a new concept is derived for HashSet?
Both ArrayList and Vector are accessed by positional index, so that there are no conflicts and access is always O(1).
A hash-based data structure is accessed by a hashed value, which can collide and degrade into access to a second-level "overflow" data structure (list or tree). If you have no such collisions, access is O(1), but if you have many collisions, it can be significantly worse. You can control this a bit by allocating more memory (so that there are more buckets and hopefully fewer collisions).
As a result, there is no need to grow an ArrayList to a capacity more than you need to store all elements, but it does make sense to "waste" a bit (or a lot) in the case of a HashSet. The parameter is exposed to allow the programmer to choose what works best for her application.
As Jonny Henly has described. It is because of the way data is stored.
ArrayList is linear data structure, while HashSet is not. In HashSet data is stored in underlying array based on hashcodes. In a way performance of HashSet is linked to how many buckets are filled and how well data is distributed among these buckets. Once this distribution of data is beyond a certain level (called load factor) re-hashing is done.
HashSet is primarily used to ensure that the basic operations (such as adding, fetching, modifying and deleting) are performed in constant time regardless of the number of entries being stored in the HashSet.
Though a well designed hash function can achieve this, designing one might take time. So if performance is a critical requirement for the application, we could use the load factor to ensure the operations are performed in constant time as well. I think we could call both of these as redundant's for each other (the load factor and the hash function).
I agree that this may not be a perfect explanation, but I hope it does bring some clarity on the subject.
Android have their own implementation of HashMap, which doesnt use Autoboxing and it is somehow better for performance (CPU or RAM)?
https://developer.android.com/reference/android/support/v4/util/ArrayMap.html
From what I read here, I should replace my HashMap objects with ArrayMap objects if I have HashMaps whose size is below hundreds of records and will be frequently written to. And there is no point in replacing my HashMaps with ArrayMaps if they are going to contain hundreds of objects and will be written to once and read frequently. Am I Correct?
You should take a look at this video : https://www.youtube.com/watch?v=ORgucLTtTDI
Perfect situations:
1. small number of items (< 1000) with a lots of accesses or the insertions and deletions are infrequent enough that the overhead of doing so is not really noticed.
2. containers of maps - maps of maps where the submaps tends to have low number of items and often iterate over then a lot of time.
ArrayMap uses way less memory than HashMap and is recommended for up to a few hundred items, especially if the map is not updated frequently. Spending less time allocating and freeing memory may also provide some general performance gains.
Update performance is a bit worse because any insert requires an array copy. Read performance is comparable for a small number of items and uses binary search.
Is there any reason for you to attempt such a replacement?
If it's to improve performance then you have to make measures before and after the replacement and see if the replacements helped.
Probably, not worth of the effort.
Checking in java and googling online for hashtable code examples it seems that the resizing of the table is done by doubling it.
But most textbooks say that the best size for the table is a prime number.
So my question is:
Is the approach of doubling because:
It is easy to implement, or
Is finding a prime number too inefficient (but I think that finding
the next prime going over n+=2 and testing for primality using
modulo is O(loglogN) which is cheap)
Or this is my misunderstanding and only certain hashtable variants
only require prime table size?
Update:
The way presented in textbooks using a prime number is required for certain properties to work (e.g. quadratic probing needs a prime size table to prove that e.g. if a table is not full item X will be inserted).
The link posted as duplicate asks generally about increasing by any number e.g. 25% or next prime and the answer accepted states that we double in order to keep the resizing operation "rare" so we can guarantee amortized time.
This does not answer the question of having a table size that is prime and using a prime for resizing such that is even greater than double. So the idea is to keep the properties of the prime size taking into account the resizing overhead
Q: But most textbooks say that the best size for the table is a prime number.
Regarding size primality:
What comes to primality of size, it depends on collision resolution algorithm your choose. Some algorithms require prime table size (double hashing, quadratic hashing), others don't, and they could benefit from table size of power of 2, because it allows very cheap modulo operations. However, when closest "available table sizes" differ in 2 times, memory usage of hash table might be unreliable. So, even using linear hashing or separate chaining, you can choose non power of 2 size. In this case, in turn, it's worth to choose particulary prime size, because:
If you pick prime table size (either because algorithm requires this, or because you are not satisfied with memory usage unreliability implied by power-of-2 size), table slot computation (modulo by table size) could be combined with hashing. See this answer for more.
The point that table size of power of 2 is undesirable when hash function distribution is bad (from the answer by Neil Coffey) is impractical, because even if you have bad hash function, avalanching it and still using power-of-2 size would be faster that switching to prime table size, because a single integral division is still slower on modern CPUs that several of multimplications and shift operations, required by good avalanching functions, e. g. from MurmurHash3.
Q: Also to be honest I got lost a bit on if you actually recommend primes or not. Seems that it depends on the hash table variant and the quality of the hash function?
Quality of hash function doesn't matter, you always can "improve" hash function by MurMur3 avalancing, that is cheaper than switching to prime table size from power-of-2 table size, see above.
I recommend choosing prime size, with QHash or quadratic hash algorithm (aren't same), only when you need precise control over hash table load factor and predictably high actual loads. With power-of-2 table size, minimum resize factor is 2, and generally we cannot guarantee the hash table will have actual load factor any higher than 0.5. See this answer.
Otherwise, I recommend to go with power-of-2 sized hash table with linear probing.
Q: Is the approach of doubling because:
It is easy to implement, or
Basically, in many cases, yes.
See this large answer regarding load factors:
Load factor is not an essential part of hash table data structure -- it is the way to define rules of behaviour for the dymamic system (growing/shrinking hash table is a dynamic system).
Moreover, in my opinion, in 95% of modern hash table cases this way is over simplified, dynamic systems behave suboptimally.
What is doubling? It's just the simpliest resizing strategy. The strategy could be arbitrarily complex, performing optimally in your use cases. It could consider present hash table size, growth intensity (how much get operations were done since previous resize), etc. Nobody forbids you to implement such custom resizing logic.
Q: Is finding a prime number too inefficient (but I think that finding the next prime going over n+=2 and testing for primality using modulo is O(loglogN) which is cheap)
There is a good practice to precompute some subset of prime hash table sizes, to choose between them using binary search in runtime. See the list double hash capacities and explaination, QHash capacities. Or, even using direct lookup, that is very fast.
Q: Or this is my misunderstanding and only certain hashtable variants only require prime table size?
Yes, only certain types requre, see above.
Java HashMap (java.util.HashMap) chains bucket collisions in a linked list (or [as of JDK8] tree depending on the size and overfilling of bins).
Consequently theories about secondary probing functions don't apply.
It seems the message 'use primes sizes for hash tables' has become detached from the circumstances it applies over the years...
Using powers of two has the advantage (as noted by other answers) of reducing the hash-value to a table entry can be achieved by a bit-mask. Integer division is relatively expensive and in high performance situations this can help.
I'm going to observe that "redistributing the collision chains when rehashing is a cinch for tables that are a power of two going to a power of two".
Notice that when using powers of two rehashing to twice the size 'splits' each bucket between two buckets based on the 'next' bit of the hash-code.
That is, if the hash-table had 256 buckets and so using the lowest 8 bits of the hash-value rehashing splits each collision chain based on the 9th bit and either remains in the same bucket B (9th bit is 0) or goes to bucket B+256 (9th bit is 1). Such splitting can preserve/take advantage of the bucket handling approach. For example, java.util.HashMap keeps small buckets sorted in reverse order of insertion and then splits them into two sub-structures obeying that order. It keeps big buckets in a binary tree sorted by hash-code and similarly splits the tree to preserve that order.
NB: These tricks weren't implemented until JDK8.
(I am pretty sure) Java.util.HashMap only sizes up (never down). But there are similar efficiencies to halving a hash-table as doubling it.
One 'downside' of this strategy is that Object implementers aren't explicitly required to make sure the low order bits of hash-codes are well distributed.
A perfectly valid hash-code could be well distributed overall but poorly distributed in its low order bits. So an object obeying the general contract for hashCode() might still tank when actually used in a HashMap!
Java.util.HashMap mitigates this by applying an additional hash 'spread' onto the provided hashCode() implementation. That 'spread' is really quick crude (xors the 16 high bits with the low).
Object implmenters should be aware (if not already) that bias in their hash-code (or lack thereof) can have a significant effect on the performance of data structures using hashes.
For the record I've based this analysis on this copy of the source:
http://hg.openjdk.java.net/jdk8/jdk8/jdk/file/687fd7c7986d/src/share/classes/java/util/HashMap.java
I am looking around for the best algorithms for the bitset operations like intersection and union, and found a lot of links and similar questions also.
Eg: Similar Question on Stack-Overflow
One thing however, which I am trying to understand is that where bit set stands into this. Eg, Lucene has taken BitSet operations to give a high performing set operations, specially because it can work at a lower level.
However, what looks to me is, the bit-set will start performing slow and slow, as the number of elements increase and the set is sparse, say set has ~10 elements where the max number of elements can be 2 Billion, because that will call out for unnecessary matching. What do you suggest ?
Bit Sets indeed make sense for dense sets, i.e. covering a significant fraction of the domain, as they represent every possible element. The space and running time requirements are O(D) [D = domain size = 2 billion !].
Sorted Set operations represent only the elements in the given set and will have an O(E) behavior [E = number of elements = 10], much more appropriate.
Bit Sets are fast, they are not efficient. I mean their hidden constant is smaller. They are blazingly fast for small sets (say D <= 1024) as they can process 32/64 elements in a single CPU instruction.
For sparse bitsets you can greatly improve performance (and reduce memory usage) using sparse bitmaps where you divide your data into chunks as opposed to storing everything under a single key.
When using bitmaps for analytics, you have a limited number of users active at any given time (e.g. day) and sparse bitmaps use this fact to their advantage.
Shameless plug: http://github.com/bilus/redis-bitops (if you're using Ruby but there are also performance notes there).
I'm looking to implement a B-tree (in Java) for a "one use" index where a few million keys are inserted, and queries are then made a handful of times for each key. The keys are <= 40 byte ascii strings, and the associated data always takes up 6 bytes. The B-tree structure has been chosen because my memory budget does not allow me to keep the entire temporary index in memory.
My issue is about the practical details in choosing a branching factor and storing nodes on disk. It seems to me that there are two approaches:
One node always fit within one block. Achieved by choosing a branching factor k so that even for the worst case key-length the storage requirement for keys, data and control structures are <= the system block size. k is likely to be low, and nodes will in most cases have a lot of empty room.
One node can be stored on multiple blocks. Branching factor is chosen independent of key size. Loading a single node may require that multiple blocks are loaded.
The questions are then:
Is the second approach what is usually used for variable-length keys? or is there some completely different approach I have missed?
Given my use case, would you recommend a different overall solution?
I should in closing mention that I'm aware of the jdbm3 project, and is considering using it. Will attempt to implement my own in any case, both as a learning exercise and to see if case specific optimization can yield better performance.
Edit: Reading about SB-Trees at the moment:
S(b)-Trees
Algorithms and Data Structures for External Memory
I'm missing option C here:
At least two tuples always fit into one block, the block size is chosen accordingly. Blocks are filled up with as many key/value pairs as possible, which means the branching factor is variable. If the blocksize is much greater than average size of a (key, value) tuple, the wasted space would be very low. Since the optimal IO size for discs is usually 4k or greater and you have a maximum tuple size of 46, this is automatically true in your case.
And for all options you have some variants: B* or B+ Trees (see Wikipedia).
JDBM BTree is already self balancing. It also have defragmentation which is very fast and solves all problems described above.
One node can be stored on multiple blocks. Branching factor is chosen independent of key size. Loading a single node may require that multiple blocks are loaded.
Not necessary. JDBM3 uses mapped memory, so it never reads full block from disk to memory. It creates 'a view' on top of block and only read partial data as actually needed. So instead of reading full 4KB block, it may read just 2x128 bytes. This depends on underlying OS block size.
Is the second approach what is usually used for variable-length keys? or is there some completely different approach I have missed?
I think you missed point that increasing disk size decreases performance, as more data have to be read. And single tree can have share both approaches (newly inserted nodes first, second after defragmentation).
Anyway, flat-file with mapped memory buffer is probably best for your problem. Since you have fixed record size and just a few million records.
Also have look at leveldb. It has new java port which almost beats JDBM:
https://github.com/dain/leveldb
http://code.google.com/p/leveldb/
You could avoid this hassle if you use some embedded database. Those have solved these problems and some more for you already.
You also write: "a few million keys" ... "[max] 40 byte ascii strings" and "6 bytes [associated data]". This does not count up right. One gig of RAM would allow you more then "a few million" entries.