Xcdat: Fast compressed trie dictionary library

Xcdat is a C++17 header-only library of a fast compressed string dictionary based on the improved double-array trie structure described in the paper: Compressed double-array tries for string dictionaries supporting fast lookup, Knowledge and Information Systems, 2017, available at here.

Table of contents

• Features
• Build instructions
• Command line tools
• Sample usage
• API
• Performance
• Licensing
• Todo
• References

Features

• Compressed string dictionary. Xcdat implements a (static) compressed string dictioanry that stores a set of strings (or keywords) in a compressed space while supporting several search operations [1,2]. For example, Xcdat can store an entire set of English Wikipedia titles at half the size of the raw data.
• Fast and compact data structure. Xcdat employs the double-array trie [3] known as the fastest data structure for trie implementation. However, the double-array trie resorts to many pointers and consumes a large amount of memory. To address this, Xcdat applies the XCDA method [2] that represents the double-array trie in a compressed format while maintaining the fast searches.
• Cache efficiency. Xcdat employs a minimal-prefix trie [4] that replaces redundant trie nodes into strings, resulting in reducing random access and improving locality of references.
• Dictionary encoding. Xcdat maps N distinct keywords into unique IDs from [0,N-1], and supports the two symmetric operations: lookup returns the ID corresponding to a given keyword; decode returns the keyword associated with a given ID. The mapping is so-called dictionary encoding (or domain encoding) and is fundamental in many DB applications as described by Martínez-Prieto et al [1] or Müller et al. [5].
• Prefix search operations. Xcdat supports prefix search operations realized by trie search algorithms: prefix_search returns all the keywords contained as prefixes of a given string; predictive search returns all the keywords starting with a given string. These will be useful in many NLP applications such as auto completions [6], stemmed searches [7], or morphological analysis [8].
• 64-bit support. As mentioned before, since the double array is a pointer-based data structure, most double-array libraries use 32-bit pointers to reduce memory consumption, resulting in limiting the scale of the input dataset. On the other hand, the XCDA method allows Xcdat to represent 64-bit pointers without sacrificing memory efficiency.
• Binary key support. In normal mode, Xcdat will use the \0 character as an end marker for each keyword. However, if the dataset include \0 characters, it will use bit flags instead of end markers, allowing the dataset to consist of binary keywords.
• Memory mapping. Xcdat supports memory mapping, allowing data to be deserialized quickly without loading it into memory. Of course, deserialization by the loading is also supported.
• Header only. The library consists only of header files, and you can easily install it.

Build instructions

You can download, compile, and install Xcdat with the following commands.

$ git clone https://github.com/kampersanda/xcdat.git
$ cd xcdat
$ mkdir build
$ cd build
$ cmake ..
$ make -j
$ make install

Or, since this library consists only of header files, you can easily install it by passing through the path to the directory include.

Requirements

You need to install a modern C++17 ready compiler such as g++ >= 7.0 or clang >= 4.0. For the build system, you need to install CMake >= 3.0 to compile the library.

The library considers a 64-bit operating system. The code has been tested only on Mac OS X and Linux. That is, this library considers only UNIX-compatible OS.

Command line tools

Xcdat provides command line tools to build the index and perform searches, which are inspired by marisa-trie. All the tools will print the command line options by specifying the parameter -h.

xcdat_build

It builds the trie index from a given dataset consisting of keywords separated by newlines. The following command builds the trie index from dataset enwiki-titles.txt and writes the index into file idx.bin.

$ xcdat_build enwiki-titles.txt idx.bin
Number of keys: 15955763
Number of trie nodes: 36441058
Number of DA units: 36520704
Memory usage in bytes: 1.70618e+08
Memory usage in MiB: 162.714

xcdat_lookup

It tests the lookup operation for a given index. Given a query string via stdin, it prints the associated ID if found, or -1 otherwise.

$ xcdat_lookup idx.bin
Algorithm
1255938	Algorithm
Double_Array
-1	Double_Array

xcdat_decode

It tests the decode operation for a given index. Given a query ID via stdin, it prints the corresponding keyword if the ID is in the range [0,N-1], where N is the number of stored keywords.

$ xcdat_decode idx.bin
1255938
1255938	Algorithm

xcdat_prefix_search

It tests the prefix_search operation for a given index. Given a query string via stdin, it prints all the keywords contained as prefixes of a given string.

$ xcdat_prefix_search idx.bin
Algorithmic
6 found
57	A
798460	Al
1138004	Alg
1253024	Algo
1255938	Algorithm
1255931	Algorithmic

xcdat_predictive_search

It tests the predictive_search operation for a given index. Given a query string via stdin, it prints the first n keywords starting with a given string, where n is one of the parameters.

$ xcdat_predictive_search idx.bin -n 3
Algorithm
263 found
1255938	Algorithm
1255944	Algorithm's_optimality
1255972	Algorithm_(C++)

xcdat_enumerate

It prints all the keywords stored in a given index.

$ xcdat_enumerate idx.bin | head -3
0	!
107	!!
138	!!!

xcdat_benchmark

It measures the performances of possible tries for a given dataset. To perform search operations, it randomly samples n queires from the dataset, where n is one of the parameters.

$ xcdat_benchmark enwiki-titles.txt
** xcdat::trie_7_type **
Number of keys: 15955763
Memory usage in bytes: 1.70618e+08
Memory usage in MiB: 162.714
Construction time in seconds: 12.907
Lookup time in microsec/query: 0.4674
Decode time in microsec/query: 0.8722
** xcdat::trie_8_type **
Number of keys: 15955763
Memory usage in bytes: 1.64104e+08
Memory usage in MiB: 156.502
Construction time in seconds: 13.442
Lookup time in microsec/query: 0.7593
Decode time in microsec/query: 1.2341

Sample usage

sample/sample.cpp provides a sample usage.

#include <iostream>
#include <string>

#include <xcdat.hpp>

int main() {
    // Input keys
    std::vector<std::string> keys = {
        "AirPods",  "AirTag",  "Mac",  "MacBook", "MacBook_Air", "MacBook_Pro",
        "Mac_Mini", "Mac_Pro", "iMac", "iPad",    "iPhone",      "iPhone_SE",
    };

    // The input keys must be sorted and unique (although they have already satisfied in this case).
    std::sort(keys.begin(), keys.end());
    keys.erase(std::unique(keys.begin(), keys.end()), keys.end());

    const char* index_filename = "tmp.idx";

    // The trie index type
    using trie_type = xcdat::trie_8_type;

    // Build and save the trie index.
    {
        const trie_type trie(keys);
        xcdat::save(trie, index_filename);
    }

    // Load the trie index.
    const auto trie = xcdat::load<trie_type>(index_filename);

    // Basic statistics
    std::cout << "NumberKeys: " << trie.num_keys() << std::endl;
    std::cout << "MaxLength: " << trie.max_length() << std::endl;
    std::cout << "AlphabetSize: " << trie.alphabet_size() << std::endl;
    std::cout << "Memory: " << xcdat::memory_in_bytes(trie) << " bytes" << std::endl;

    // Lookup IDs from keys
    {
        const auto id = trie.lookup("Mac_Pro");
        std::cout << "Lookup(Mac_Pro) = " << id.value_or(UINT64_MAX) << std::endl;
    }
    {
        const auto id = trie.lookup("Google_Pixel");
        std::cout << "Lookup(Google_Pixel) = " << id.value_or(UINT64_MAX) << std::endl;
    }

    // Decode keys from IDs
    {
        const auto dec = trie.decode(4);
        std::cout << "Decode(4) = " << dec << std::endl;
    }

    // Common prefix search
    {
        std::cout << "CommonPrefixSearch(MacBook_Air) = {" << std::endl;
        auto itr = trie.make_prefix_iterator("MacBook_Air");
        while (itr.next()) {
            std::cout << "   (" << itr.decoded_view() << ", " << itr.id() << ")," << std::endl;
        }
        std::cout << "}" << std::endl;
    }

    // Predictive search
    {
        std::cout << "PredictiveSearch(Mac) = {" << std::endl;
        auto itr = trie.make_predictive_iterator("Mac");
        while (itr.next()) {
            std::cout << "   (" << itr.decoded_view() << ", " << itr.id() << ")," << std::endl;
        }
        std::cout << "}" << std::endl;
    }

    // Enumerate all the keys (in lex order).
    {
        std::cout << "Enumerate() = {" << std::endl;
        auto itr = trie.make_enumerative_iterator();
        while (itr.next()) {
            std::cout << "   (" << itr.decoded_view() << ", " << itr.id() << ")," << std::endl;
        }
        std::cout << "}" << std::endl;
    }

    std::remove(index_filename);
    return 0;
}

The output will be

NumberKeys: 12
MaxLength: 11
AlphabetSize: 20
Memory: 1762 bytes
Lookup(Mac_Pro) = 7
Lookup(Google_Pixel) = 18446744073709551615
Decode(4) = MacBook_Air
CommonPrefixSearch(MacBook_Air) = {
   (Mac, 1),
   (MacBook, 2),
   (MacBook_Air, 4),
}
PredictiveSearch(Mac) = {
   (Mac, 1),
   (MacBook, 2),
   (MacBook_Air, 4),
   (MacBook_Pro, 11),
   (Mac_Mini, 5),
   (Mac_Pro, 7),
}
Enumerate() = {
   (AirPods, 0),
   (AirTag, 3),
   (Mac, 1),
   (MacBook, 2),
   (MacBook_Air, 4),
   (MacBook_Pro, 11),
   (Mac_Mini, 5),
   (Mac_Pro, 7),
   (iMac, 10),
   (iPad, 6),
   (iPhone, 8),
   (iPhone_SE, 9),
}

API

xcdat.hpp provides

• xcdat::trie_7_type:
• xcdat::trie_8_type:

Dictionary class

template <class BcVector>
class trie {
  public:
    using trie_type = trie<BcVector>;
    using bc_vector_type = BcVector;

    static constexpr auto l1_bits = bc_vector_type::l1_bits;

  public:
    //! Default constructor
    trie() = default;

    //! Default destructor
    virtual ~trie() = default;

    //! Copy constructor (deleted)
    trie(const trie&) = delete;

    //! Copy constructor (deleted)
    trie& operator=(const trie&) = delete;

    //! Move constructor
    trie(trie&&) noexcept = default;

    //! Move constructor
    trie& operator=(trie&&) noexcept = default;

    //! Build the trie from the input keywords, which are lexicographically sorted and unique.
    //! If bin_mode = false, the NULL character is used for the termination of a keyword.
    //! If bin_mode = true, bit flags are used istead, and the keywords can contain NULL characters.
    //! If the input keywords contain NULL characters, bin_mode will be forced to be set to true.
    template <class Strings>
    trie(const Strings& keys, bool bin_mode = false);

    //! Check if the binary mode.
    bool bin_mode() const;

    //! Get the number of stored keywords.
    std::uint64_t num_keys() const;

    //! Get the alphabet size.
    std::uint64_t alphabet_size() const;

    //! Get the maximum length of keywords.
    std::uint64_t max_length() const;

    //! Get the number of trie nodes.
    std::uint64_t num_nodes() const;

    //! Get the number of DA units.
    std::uint64_t num_units() const;

    //! Get the number of unused DA units.
    std::uint64_t num_free_units() const;

    //! Get the number of unused DA units.
    std::uint64_t tail_length() const;

    //! Lookup the ID of the keyword.
    std::optional<std::uint64_t> lookup(std::string_view key) const;

    //! Decode the keyword associated with the ID.
    std::string decode(std::uint64_t id) const;

    //! Decode the keyword associated with the ID.
    void decode(std::uint64_t id, std::string& decoded) const;

    //! An iterator class for common prefix search.
    class prefix_iterator {
      public:
        prefix_iterator() = default;

        //! Increment the iterator.
        //! Return false if the iteration is terminated.
        bool next();

        //! Get the result ID.
        std::uint64_t id() const;

        //! Get the result keyword.
        std::string decoded() const;

        //! Get the reference to the result keyword.
        //! Note that the referenced data will be changed in the next iteration.
        std::string_view decoded_view() const;
    };

    //! Make the common prefix searcher for the given keyword.
    prefix_iterator make_prefix_iterator(std::string_view key) const;

    //! Preform common prefix search for the keyword.
    void prefix_search(std::string_view key, const std::function<void(std::uint64_t, std::string_view)>& fn) const;

    //! An iterator class for predictive search.
    class predictive_iterator {
      public:
        predictive_iterator() = default;

        //! Increment the iterator.
        //! Return false if the iteration is terminated.
        bool next();

        //! Get the result ID.
        std::uint64_t id() const;

        //! Get the result keyword.
        std::string decoded() const;

        //! Get the reference to the result keyword.
        //! Note that the referenced data will be changed in the next iteration.
        std::string_view decoded_view() const;
    };

    //! Make the predictive searcher for the keyword.
    predictive_iterator make_predictive_iterator(std::string_view key) const;

    //! Preform predictive search for the keyword.
    void predictive_search(std::string_view key, const std::function<void(std::uint64_t, std::string_view)>& fn) const;

    //! An iterator class for enumeration.
    using enumerative_iterator = predictive_iterator;

    //! An iterator class for enumeration.
    enumerative_iterator make_enumerative_iterator() const;

    //! Enumerate all the keywords and their IDs stored in the trie.
    void enumerate(const std::function<void(std::uint64_t, std::string_view)>& fn) const;

    //! Visit the members.
    template <class Visitor>
    void visit(Visitor& visitor);
};

I/O handlers

xcdat.hpp provides some functions for handling I/O operations.

template <class Trie>
Trie mmap(const char* address);

Performance

To be added...

Licensing

This library is free software provided under the MIT License.

If you use the library in academic settings, please cite the following paper.

@article{kanda2017compressed,
    title={Compressed double-array tries for string dictionaries supporting fast lookup},
    author={Kanda, Shunsuke and Morita, Kazuhiro and Fuketa, Masao},
    journal={Knowledge and Information Systems (KAIS)},
    volume={51},
    number={3},
    pages={1023--1042},
    year={2017},
    publisher={Springer}
}

Todo

• Support other language bindings.
• Add SIMD-ization.

References

1. J. Aoe. An efficient digital search algorithm by using a double-array structure. IEEE Transactions on Software Engineering, 15(9):1066–1077, 1989.
2. N. R. Brisaboa, S. Ladra, and G. Navarro. DACs: Bringing direct access to variable-length codes. Information Processing & Management, 49(1):392–404, 2013.
3. S. Kanda, K. Morita, and M. Fuketa. Compressed double-array tries for string dictionaries supporting fast lookup. Knowledge and Information Systems, 51(3): 1023–1042, 2017.
4. M. A. Martínez-Prieto, N. Brisaboa, R. Cánovas, F. Claude, and G. Navarro. Practical compressed string dictionaries. Information Systems, 56:73–108, 2016
5. S. Yata, M. Oono, K. Morita, M. Fuketa, T. Sumitomo, and J. Aoe. A compact static double-array keeping character codes. Information Processing & Management, 43(1):237–247, 2007.