PTHash is a C++ library implementing fast and compact minimal perfect hash functions as described in the papers

• PTHash: Revisiting FCH Minimal Perfect Hashing [1]
• Parallel and External-Memory Construction of Minimal Perfect Hash Functions with PTHash [2]

Please, cite these papers if you use PTHash.

• The PHOBIC branch of PTHash introduces some algorithmic novelties to build smaller functions and accelerate construction.

• Minimal and Non-Minimal Perfect Hash Functions
• Space/Time Efficiency: fast lookup within compressed space
• External-Memory Scaling
• Multi-Threaded Construction
• Configurable: can offer different trade-offs (between construction time, lookup time, and space effectiveness)

Given a set S of n distinct keys, a function f that bijectively maps the keys of S into the first n natural numbers is called a minimal perfect hash function (MPHF) for S. Algorithms that find such functions when n is large and retain constant evaluation time are of practical interest. For instance, search engines and databases typically use minimal perfect hash functions to quickly assign identifiers to static sets of variable-length keys such as strings. The challenge is to design an algorithm which is efficient in three different aspects: time to find f (construction time), time to evaluate f on a key of S (lookup time), and space of representation for f.

PTHash is one such algorithm.

The following guide is meant to provide a brief overview of the library by illustrating its functionalities through some examples.

• Integration
• Compiling the Code
• Quick Start
• Build Examples
• An Example Benchmark
• Other Resources
• Authors
• References

Integrating PTHash in your own project is very simple: just get the source code and include the header include/pthash.hpp in your code. No other configurations are needed.

If you use git, the easiest way to add PTHash is via git add submodule as follows.

git submodule add https://github.com/jermp/pthash.git

The code is tested on Linux with gcc and on Mac OS with clang (both Intel and ARM processors, like Apple M1). To build the code, CMake is required.

Clone the repository with

git clone --recursive https://github.com/jermp/pthash.git

If you have cloned the repository without --recursive, be sure you pull the dependencies with the following command before compiling:

git submodule update --init --recursive

To compile the code for a release environment (see file CMakeLists.txt for the used compilation flags), it is sufficient to do the following:

mkdir build
cd build
cmake ..
make -j

For a testing environment, use the following instead:

mkdir debug_build
cd debug_build
cmake .. -D CMAKE_BUILD_TYPE=Debug -D PTHASH_USE_SANITIZERS=On
make

(NOTE: Beware that the software will result in a much slower execution when running in debug mode and using sanitizers. Use this only for debug purposes, not to run performance tests.)

By default, you can choose between three encoders to compress the PTHash data structure: partitioned_compact, dictionary_dictionary, and elias_fano, respectively indicated with PC, D-D, and EF in our papers.

If you want to test all the encoders we tested in the SIGIR paper [1], you can compile with

cmake .. -D PTHASH_ENABLE_ALL_ENCODERS=On

By default, PTHash assumes there are less than $2^{32}$ buckets, hence 32-bit integers are used for bucket ids. To overcome this, you can either lower the value of c or recompile with

cmake .. -D PTHASH_ENABLE_LARGE_BUCKET_ID_TYPE=On

to use 64-bit integers for bucket ids.

For a quick start, see the source file src/example.cpp (reported below). The example shows how to setup a simple build configuration for PTHash (parameters, base hasher, and encoder).

After compilation, run this example with

./example

which will build a PTHash MPHF on 10M random 64-bit keys using c = 6.0 and alpha = 0.94. It also shows how to serialize the data structure on disk and re-load it for evaluation.

#include <iostream>
#include "../include/pthash.hpp"
#include "util.hpp"  // for functions distinct_keys and check

int main() {
    using namespace pthash;

    /* Generate 10M random 64-bit keys as input data. */
    static const uint64_t num_keys = 10000000;
    static const uint64_t seed = 1234567890;
    std::cout << "generating input data..." << std::endl;
    std::vector<uint64_t> keys = distinct_keys<uint64_t>(num_keys, seed);
    assert(keys.size() == num_keys);

    /* Set up a build configuration. */
    build_configuration config;
    config.c = 6.0;
    config.alpha = 0.94;
    config.minimal_output = true;  // mphf
    config.verbose_output = true;

    /* Declare the PTHash function. */
    typedef single_phf<murmurhash2_64,         // base hasher
                       dictionary_dictionary,  // encoder type
                       true                    // minimal
                       > pthash_type;
    pthash_type f;

    /* Build the function in internal memory. */
    std::cout << "building the function..." << std::endl;
    f.build_in_internal_memory(keys.begin(), keys.size(), config);

    /* Compute and print the number of bits spent per key. */
    double bits_per_key = static_cast<double>(f.num_bits()) / f.num_keys();
    std::cout << "function uses " << bits_per_key << " [bits/key]" << std::endl;

    /* Sanity check! */
    if (check(keys.begin(), keys.size(), f)) std::cout << "EVERYTHING OK!" << std::endl;

    /* Now evaluate f on some keys. */
    for (uint64_t i = 0; i != 10; ++i) {
        std::cout << "f(" << keys[i] << ") = " << f(keys[i]) << '\n';
    }

    /* Serialize the data structure to a file. */
    std::cout << "serializing the function to disk..." << std::endl;
    std::string output_filename("pthash.bin");
    essentials::save(f, output_filename.c_str());

    /* Now reload from disk and query. */
    pthash_type other;
    essentials::load(other, output_filename.c_str());
    for (uint64_t i = 0; i != 10; ++i) {
        std::cout << "f(" << keys[i] << ") = " << other(keys[i]) << '\n';
        assert(f(keys[i]) == other(keys[i]));
    }

    std::remove(output_filename.c_str());
    return 0;
}

All the examples below must be run from within the directory where the code was compiled (see the section Compiling the Code), using the driver program called build.

Running the command

./build --help

shows the usage of the driver program, as reported below.

Usage: ./build [-h,--help] [-n num_keys] [-c c] [-a alpha] [-e encoder_type] [-p num_partitions] [-s seed] [-t num_threads] [-i input_filename] [-o output_filename] [-d tmp_dir] [-m ram] [--minimal] [--external] [--verbose] [--check] [--lookup]

[-n num_keys]
REQUIRED: The size of the input.

[-c c]
REQUIRED: A constant that trades construction speed for space effectiveness. A reasonable value lies between 3.0 and 10.0.

[-a alpha]
REQUIRED: The table load factor. It must be a quantity > 0 and <= 1.

[-e encoder_type]
REQUIRED: The encoder type. Possibile values are: 'compact', 'partitioned_compact', 'compact_compact', 'dictionary', 'dictionary_dictionary', 'elias_fano', 'dictionary_elias_fano', 'sdc', 'all'.
The 'all' type will just benchmark all encoders. (Useful for benchmarking purposes.)

[-p num_partitions]
Number of partitions.

[-s seed]
Seed to use for construction.

[-t num_threads]
Number of threads to use for construction.

[-i input_filename]
A string input file name. If this is not provided, then num_keys 64-bit random keys will be used as input instead.If, instead, the filename is '-', then input is read from standard input.

[-o output_filename]
Output file name where the function will be serialized.

[-d tmp_dir]
Temporary directory used for building in external memory. Default is directory '.'.

[-m ram]
Number of Giga bytes of RAM to use for construction in external memory.

[--minimal]
Build a minimal PHF.

[--external]
Build the function in external memory.

[--verbose]
Verbose output during construction.

[--check]
Check correctness after construction.

[--lookup]
Measure average lookup time after construction.

[-h,--help]
Print this help text and silently exits.

./build -n 1000000 -c 4.5 -a 0.99 -e dictionary_dictionary -s 727369 --minimal --verbose --check --lookup -o mphf.bin

This example will build a MPHF over 1M random 64-bit keys (generated with seed 727369), using c = 4.5, alpha = 0.99, and compressing the MPHF data structure with the encoder dictionary_dictionary.

The data structure will be serialized on a binary file named mphf.bin.

It will also check the correctness of the data structure (flag --check) and measure average lookup time (flag --lookup).

Construction will happen in internal memory, using a single processing thread. (Experimental setting of the SIGIR paper [1].)

For the following example, we are going to use the strings from the UK-2005 URLs collection, which can be downloaded by clicking here. (This is also one of the datasets used in the paper.)

The file is ~300 MB compressed using gzip (2.86 GB uncompressed).

After download, place the dataset in the build directory and run

gunzip uk-2005.urls.gz

to uncompress it. The file contains one string per line, for a total of 39,459,925 strings.

The following command will build a MPHF using the strings of the file as input keys, with c = 7.0, alpha = 0.94.

./build -n 39459925 -c 7.0 -a 0.94 -e dictionary_dictionary -s 1234567890 --minimal -i uk-2005.urls --verbose --check --lookup

./build -n 39459925 -c 7.0 -a 0.94 -e dictionary_dictionary -s 1234567890 --minimal -i uk-2005.urls --verbose --check --lookup -p 128

This example will run the construction over the same input and parameters used in Example 2, but with 128 partitions. The resulting data structure will consume essentially the same space as that built in Example 2 and only slightly slower at lookup.

./build -n 39459925 -c 7.0 -a 0.94 -e dictionary_dictionary -s 1234567890 -i uk-2005.urls --verbose --check --lookup --external

This example will run the construction over the same input and parameters used in Example 2, but using external memory. The resulting data structure will be exactly the same as that built in Example 2.

You can always specify to use multiple threads for construction with -t. For example, just append -t 4 to any of the previous build commands to use 4 parallel threads. (Also consult our second paper [2] for more information about parallelism.)

Just do not specify the --minimal flag when using the build tool.

You can make the build tool read the keys from stardard input using bash pipelining (|) in combination with option -i -. This is very useful when building keys from compressed files.

Some examples below.

for i in $(seq 1 1000000) ; do echo $i ; done > foo.txt
cat foo.txt | ./build --minimal -c 5 -a 0.94 -e dictionary_dictionary -n 1000000 -m 1 -i - -o foo.mph --verbose --external

gzip foo.txt
zcat foo.txt.gz | ./build --minimal -c 5 -a 0.94 -e dictionary_dictionary -n 1000000 -m 1 -i - -o foo.mph --verbose --external

gunzip foo.txt.gz
zstd foo.txt
zstdcat foo.txt.zst | ./build --minimal -c 5 -a 0.94 -e dictionary_dictionary -n 1000000 -m 1 -i - -o foo.mph --verbose --external

Note: you may need to write zcat < foo.txt.gz | (...) on Mac OSX.

One caveat of this approach is that is not possible to use --check nor --lookup because these two options need to re-iterate over the keys from the stream.

The script script/run_benchmark.sh runs the 4 trade-off configurations (encoder, alpha, c) described in Section 5.2 of the paper [1] on 100M and 1000M keys.

C-C stands for "compact-compact" encoder; D-D for "dictionary-dictionary"; and EF for "Elias-Fano".

Be sure you run the benchmark after compiling with

cmake .. -D PTHASH_ENABLE_ALL_ENCODERS=On

From within the directory where the code has been compiled, just run

bash ../script/run_benchmark.sh 2> results.json

to reproduce the bottom part of Table 5 of the SIGIR 2021 paper [1]. (All constructions run in internal memory on a single core of the processor).

Below, the result of the benchmark across different processors and compilers. The code is compiled with -O3 and -march=native in all cases.

• We maintain a benchmark to evaluate MPHF algorithms available at

  https://github.com/roberto-trani/mphf_benchmark.

  This benchmark was also used for the experiments in the SIGIR 2021 paper [1].

• If you want an overview of the algorithm, you can consult these slides.

• Giulio Ermanno Pibiri, giulioermanno.pibiri@unive.it
• Roberto Trani, roberto.trani@isti.cnr.it

• [1] Giulio Ermanno Pibiri and Roberto Trani. "PTHash: Revisiting FCH Minimal Perfect Hashing". In Proceedings of the 44th International Conference on Research and Development in Information Retrieval (SIGIR). 2021.
• [2] Giulio Ermanno Pibiri and Roberto Trani. "Parallel and External-Memory Construction of Minimal Perfect Hash Functions with PTHash". Transactions on Knowledge and Data Engineering (TKDE). 2023.