succinctrits

This library provides succinct Rank/Select data structures on trits (i.e., ternary digits). A vector consisting of n values from {0,1,2} is stored in 1.6n bits of space, which is close to the theoretically-optimal space usage of 1.57n bits [1]. The Rank/Select data structures are implemented in 0.32n additional bits of space in a similar manner to traditional approaches for bit vectors (e.g., [2]).

The trit-vector implementation is based on Fischer's approach presented in [3].

Install

This library consists of only header files. Please pass the path to the directory succinctrits/include.

Sample usage

#include <iostream>
#include <random>

#include <rs_support.hpp>
#include <trit_vector.hpp>

int main() {
    std::vector<uint8_t> trits = {1, 0, 1, 2, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 2, 1, 2, 0, 1};
    succinctrits::trit_vector tv(trits.begin(), trits.size());

    std::cout << "=== Trie Array ===" << std::endl;
    std::cout << "addr: ";
    for (uint64_t i = 0; i < tv.get_num_trits(); ++i) {
        std::cout << i % 10 << ' ';
    }
    std::cout << std::endl << "trit: ";
    for (uint64_t i = 0; i < tv.get_num_trits(); ++i) {
        std::cout << uint32_t(tv[i]) << ' ';
    }
    std::cout << std::endl;

    succinctrits::rs_support<0> tv_rs_0(&tv);
    succinctrits::rs_support<1> tv_rs_1(&tv);
    succinctrits::rs_support<2> tv_rs_2(&tv);

    std::cout << "=== Operations ===" << std::endl;
    std::cout << "rank_0(6)   = " << tv_rs_0.rank(6) << std::endl;
    std::cout << "rank_1(10)  = " << tv_rs_1.rank(10) << std::endl;
    std::cout << "rank_2(3)   = " << tv_rs_2.rank(3) << std::endl;
    std::cout << "select_0(3) = " << tv_rs_0.select(3) << std::endl;
    std::cout << "select_1(5) = " << tv_rs_1.select(5) << std::endl;
    std::cout << "select_2(0) = " << tv_rs_2.select(0) << std::endl;

    std::cout << "=== Statistics ===" << std::endl;
    std::cout << "num trits: " << tv.get_num_trits() << std::endl;
    std::cout << "num 0s:    " << tv_rs_0.get_num_target_trits() << std::endl;
    std::cout << "num 1s:    " << tv_rs_1.get_num_target_trits() << std::endl;
    std::cout << "num 2s:    " << tv_rs_2.get_num_target_trits() << std::endl;

    {
        std::ofstream ofs("trits.idx");
        tv.save(ofs);
        tv_rs_0.save(ofs);
        tv_rs_1.save(ofs);
        tv_rs_2.save(ofs);
    }

    {
        std::ifstream ifs("trits.idx");
        succinctrits::trit_vector other_tv;
        succinctrits::rs_support<0> other_tv_rs_0;
        succinctrits::rs_support<1> other_tv_rs_1;
        succinctrits::rs_support<2> other_tv_rs_2;
        other_tv.load(ifs);
        other_tv_rs_0.load(ifs);
        other_tv_rs_1.load(ifs);
        other_tv_rs_2.load(ifs);
        other_tv_rs_0.set_vector(&other_tv);
        other_tv_rs_1.set_vector(&other_tv);
        other_tv_rs_2.set_vector(&other_tv);
    }

    std::remove("trits.idx");
    return 0;
}

The output will be

=== Trie Array ===
addr: 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 
trit: 1 0 1 2 1 0 0 1 0 1 0 0 1 1 1 2 1 2 0 1 
=== Operations ===
rank_0(6)   = 2
rank_1(10)  = 5
rank_2(3)   = 0
select_0(3) = 8
select_1(5) = 12
select_2(0) = 3
=== Statistics ===
num trits: 20
num 0s:    7
num 1s:    10
num 2s:    3

Benchmark

• 3.5 GHz Intel Core i7
• 16 GB 2133 MHz LPDDR3
• OS X 10.14.6
• Apple clang version 11.0.0

$ ./benchmark/benchmark 
=== Benchmark for 1000000 trits ===
# access time: 19.3666 ns/op
# rank time:   34.0611 ns/op
# select time: 117.213 ns/op
# trit_vector: 1.60006 bits/trit
# rs_support:  0.321088 bits/trit
=== Benchmark for 10000000 trits ===
# access time: 27.337 ns/op
# rank time:   43.6852 ns/op
# select time: 143.572 ns/op
# trit_vector: 1.60001 bits/trit
# rs_support:  0.320986 bits/trit
=== Benchmark for 100000000 trits ===
# access time: 23.5833 ns/op
# rank time:   76.2127 ns/op
# select time: 241.136 ns/op
# trit_vector: 1.6 bits/trit
# rs_support:  0.320977 bits/trit

References

1. Mihai Patrascu. Succincter. In FOCS, pages 305–313, 2008.
2. Rodrigo González, Szymon Grabowski, Veli Mäkinen, and Gonzalo Navarro. Practical implementation of rank and select queries. In WEA, pages 27–38, 2005.
3. Johannes Fischer and Daniel Peters. GLOUDS: Representing tree-like graphs. J. Discrete Algorithm., 36:39–49, 2016.