A perfect hash function maps a static set of n keys into a set of m integer numbers without collisions, where m is greater than or equal to n. If m is equal to n, the function is called minimal.
[Minimal perfect hash functions concepts.html] are widely used for memory efficient storage and fast retrieval of items from static sets, such as words in natural languages, reserved words in programming languages or interactive systems, universal resource locations (URLs) in Web search engines, or item sets in data mining techniques. Therefore, there are applications for minimal perfect hash functions in information retrieval systems, database systems, language translation systems, electronic commerce systems, compilers, operating systems, among others.
The use of minimal perfect hash functions is, until now, restricted to scenarios where the set of keys being hashed is small, because of the limitations of current algorithms. But in many cases, to deal with huge set of keys is crucial. So, this project gives to the free software community an API that will work with sets in the order of billion of keys.
Probably, the most interesting application for minimal perfect hash functions is its use as an indexing structure for databases. The most popular data structure used as an indexing structure in databases is the B+ tree. In fact, the B+ tree is very used for dynamic applications with frequent insertions and deletions of records. However, for applications with sporadic modifications and a huge number of queries the B+ tree is not the best option, because practical deployments of this structure are extremely complex, and perform poorly with very large sets of keys such as those required for the new frontiers [database applications http://acmqueue.com/modules.php?name=Content&pa=showpage&pid=299].
For example, in the information retrieval field, the work with huge collections is a daily task. The simple assignment of ids to web pages of a collection can be a challenging task. While traditional databases simply cannot handle more traffic once the working set of web page urls does not fit in main memory anymore, minimal perfect hash functions can easily scale to hundred of millions of entries, using stock hardware.
As there are lots of applications for minimal perfect hash functions, it is important to implement memory and time efficient algorithms for constructing such functions. The lack of similar libraries in the free software world has been the main motivation to create the C Minimal Perfect Hashing Library ([gperf is a bit different gperf.html], since it was conceived to create very fast perfect hash functions for small sets of keys and CMPH Library was conceived to create minimal perfect hash functions for very large sets of keys). C Minimal Perfect Hashing Library is a portable LGPLed library to generate and to work with very efficient minimal perfect hash functions.
The CMPH Library encapsulates the newest and more efficient algorithms in an easy-to-use, production-quality, fast API. The library was designed to work with big entries that cannot fit in the main memory. It has been used successfully for constructing minimal perfect hash functions for sets with more than 100 million of keys, and we intend to expand this number to the order of billion of keys. Although there is a lack of similar libraries, we can point out some of the distinguishable features of the CMPH Library:
- It is the fastest algorithm to build PHFs and MPHFs in linear time.
- It generates the most compact PHFs and MPHFs we know of.
- It can generate PHFs with a load factor up to //99 %//.
- It can be used to generate //t//-perfect hash functions. A //t//-perfect hash function allows at most //t// collisions in a given bin. It is a well-known fact that modern memories are organized as blocks which constitute transfer unit. Example of such blocks are cache lines for internal memory or sectors for hard disks. Thus, it can be very useful for devices that carry out I/O operations in blocks.
- It is a two level scheme. It uses a first level hash function to split the key set in buckets of average size determined by a parameter //b// in the range //[1,32]//. In the second level it uses displacement values to resolve the collisions that have given rise to the buckets.
- It can generate MPHFs that can be stored in approximately //2.07// bits per key.
- For a load factor equal to the maximum one that is achieved by the BDZ algorithm (//81 %//), the resulting PHFs are stored in approximately //1.40// bits per key.
%html% - [BDZ Algorithm bdz.html]:
%txt% - BDZ Algorithm:
- It is very simple and efficient. It outperforms all the ones below.
- It constructs both PHFs and MPHFs in linear time.
- The maximum load factor one can achieve for a PHF is //1/1.23//.
- It is based on acyclic random 3-graphs. A 3-graph is a generalization of a graph where each edge connects 3 vertices instead of only 2.
- The resulting MPHFs are not order preserving.
- The resulting MPHFs can be stored in only //(2 + x)cn// bits, where //c// should be larger than or equal to //1.23// and //x// is a constant larger than //0// (actually, x = 1/b and b is a parameter that should be larger than 2). For //c = 1.23// and //b = 8//, the resulting functions are stored in approximately 2.6 bits per key.
- For its maximum load factor (//81 %//), the resulting PHFs are stored in approximately //1.95// bits per key.
%html% - [BMZ Algorithm bmz.html]:
%txt% - BMZ Algorithm:
- Construct MPHFs in linear time.
- It is based on cyclic random graphs. This makes it faster than the CHM algorithm.
- The resulting MPHFs are not order preserving.
- The resulting MPHFs are more compact than the ones generated by the CHM algorithm and can be stored in //4cn// bytes, where //c// is in the range //[0.93,1.15]//.
%html% - [BRZ Algorithm brz.html]:
%txt% - BRZ Algorithm:
- A very fast external memory based algorithm for constructing minimal perfect hash functions for sets in the order of billions of keys.
- It works in linear time.
- The resulting MPHFs are not order preserving.
- The resulting MPHFs can be stored using less than //8.0// bits per key.
%html% - [CHM Algorithm chm.html]:
%txt% - CHM Algorithm:
- Construct minimal MPHFs in linear time.
- It is based on acyclic random graphs
- The resulting MPHFs are order preserving.
- The resulting MPHFs are stored in //4cn// bytes, where //c// is greater than 2.
%html% - [FCH Algorithm fch.html]:
%txt% - FCH Algorithm:
- Construct minimal perfect hash functions that require less than 4 bits per key to be stored.
- The resulting MPHFs are very compact and very efficient at evaluation time
- The algorithm is only efficient for small sets.
- It is used as internal algorithm in the BRZ algorithm to efficiently solve larger problems and even so to generate MPHFs that require approximately 4.1 bits per key to be stored. For that, you just need to set the parameters -a to brz and -c to a value larger than or equal to 2.6.
- [The CHD algorithm chd.html], which is an algorithm that can be tuned to generate MPHFs that require approximately 2.07 bits per key to be stored. The algorithm outperforms [the BDZ algorithm bdz.html] and therefore is the fastest one available in the literature for sets that can be treated in internal memory.
- [The CHD_PH algorithm chd.html], which is an algorithm to generate PHFs with load factor up to //99 %//. It is actually the CHD algorithm without the ranking step. If we set the load factor to //81 %//, which is the maximum that can be obtained with [the BDZ algorithm bdz.html], the resulting functions can be stored in //1.40// bits per key. The space requirement increases with the load factor.
- All reported bugs and suggestions have been corrected and included as well.
- [An algorithm to generate MPHFs that require around 2.6 bits per key to be stored bdz.html], which is referred to as BDZ algorithm. The algorithm is the fastest one available in the literature for sets that can be treated in internal memory.
- [An algorithm to generate PHFs with range m = cn, for c > 1.22 bdz.html], which is referred to as BDZ_PH algorithm. It is actually the BDZ algorithm without the ranking step. The resulting functions can be stored in 1.95 bits per key for //c = 1.23// and are considerably faster than the MPHFs generated by the BDZ algorithm.
- An API to support the ability of packing a perfect hash function into a preallocated contiguous memory space. The computation of a packed function is still faster and can be easily mmapped.
Download [vector_adapter_ex1.c examples/vector_adapter_ex1.c]. This example does not work in versions below 0.6. You need to update the sources from GIT to make it work.
Download [file_adapter_ex2.c examples/file_adapter_ex2.c] and [keys.txt examples/keys.txt]. This example does not work in versions below 0.8. You need to update the sources from GIT to make it work.
