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The PGM-index

The Piecewise Geometric Model index (PGM-index) is a data structure that enables fast lookup, predecessor, range searches and updates in arrays of billions of items using orders of magnitude less space than traditional indexes while providing the same worst-case query time guarantees.

Website | Documentation | Paper | Slides | Python wrapper | A³ Lab

GitHub Workflow Status Language grade: C/C++ License GitHub stars GitHub forks Run on


This is a header-only library. It does not need to be installed. Just clone the repo with

git clone
cd PGM-index

and copy the include/pgm directory to your system's or project's include path.

The examples/simple.cpp file shows how to index and query a vector of random integers with the PGM-index:

#include <vector>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include "pgm/pgm_index.hpp"

int main() {
    // Generate some random data
    std::vector<int> data(1000000);
    std::generate(data.begin(), data.end(), std::rand);
    std::sort(data.begin(), data.end());

    // Construct the PGM-index
    const int epsilon = 128; // space-time trade-off parameter
    pgm::PGMIndex<int, epsilon> index(data);

    // Query the PGM-index
    auto q = 42;
    auto range =;
    auto lo = data.begin() + range.lo;
    auto hi = data.begin() + range.hi;
    std::cout << *std::lower_bound(lo, hi, q);

    return 0;

Run and edit this and other examples on Or run it locally via:

g++ examples/simple.cpp -std=c++17 -I./include -o simple

Classes overview

Other than the pgm::PGMIndex class in the example above, this library provides the following classes:

  • pgm::DynamicPGMIndex supports insertions and deletions.
  • pgm::MultidimensionalPGMIndex stores points in k dimensions and supports orthogonal range queries.
  • pgm::MappedPGMIndex stores data on disk and uses a PGMIndex for fast search operations.
  • pgm::CompressedPGMIndex compresses the segments to reduce the space usage of the index.
  • pgm::OneLevelPGMIndex uses a binary search on the segments rather than a recursive structure.
  • pgm::BucketingPGMIndex uses a top-level lookup table to speed up the search on the segments.
  • pgm::EliasFanoPGMIndex uses a top-level succinct structure to speed up the search on the segments.

The full documentation is available here.

Compile the tests and the tuner

After cloning the repository, build the project with

cmake . -DCMAKE_BUILD_TYPE=Release
make -j8

The test runner will be placed in test/. The tuner executable will be placed in tuner/. The benchmark executable will be placed in benchmark/.


This project is licensed under the terms of the Apache License 2.0.

If you use the library please put a link to the website and cite the following paper:

Paolo Ferragina and Giorgio Vinciguerra. The PGM-index: a fully-dynamic compressed learned index with provable worst-case bounds. PVLDB, 13(8): 1162-1175, 2020.

  Author = {Paolo Ferragina and Giorgio Vinciguerra},
  Title = {The {PGM-index}: a fully-dynamic compressed learned index with provable worst-case bounds},
  Year = {2020},
  Volume = {13},
  Number = {8},
  Pages = {1162--1175},
  Doi = {10.14778/3389133.3389135},
  Url = {},
  Issn = {2150-8097},
  Journal = {{PVLDB}}}

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