C_brute_force.hpp

/*********************************************************************
 *
 * Linear Arrangement Library - A library that implements a collection
 * algorithms for linear arrangments of graphs.
 *
 * Copyright (C) 2019 - 2023
 *
 * This file is part of Linear Arrangement Library. The full code is available
 * at:
 *      https://github.com/LAL-project/linear-arrangement-library.git
 *
 * Linear Arrangement Library is free software: you can redistribute it
 * and/or modify it under the terms of the GNU Affero General Public License
 * as published by the Free Software Foundation, either version 3 of the
 * License, or (at your option) any later version.
 *
 * Linear Arrangement Library is distributed in the hope that it will be
 * useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU Affero General Public License for more details.
 *
 * You should have received a copy of the GNU Affero General Public License
 * along with Linear Arrangement Library.  If not, see <http://www.gnu.org/licenses/>.
 *
 * Contact:
 *
 *     Lluís Alemany Puig (lalemany@cs.upc.edu)
 *         LARCA (Laboratory for Relational Algorithmics, Complexity and Learning)
 *         CQL (Complexity and Quantitative Linguistics Lab)
 *         Jordi Girona St 1-3, Campus Nord UPC, 08034 Barcelona.   CATALONIA, SPAIN
 *         Webpage: https://cqllab.upc.edu/people/lalemany/
 *
 *     Ramon Ferrer i Cancho (rferrericancho@cs.upc.edu)
 *         LARCA (Laboratory for Relational Algorithmics, Complexity and Learning)
 *         CQL (Complexity and Quantitative Linguistics Lab)
 *         Office S124, Omega building
 *         Jordi Girona St 1-3, Campus Nord UPC, 08034 Barcelona.   CATALONIA, SPAIN
 *         Webpage: https://cqllab.upc.edu/people/rferrericancho/
 *
 ********************************************************************/
 
// C++ includes
#if defined DEBUG
#include <cassert>
#endif
#include <vector>
 
// lal includes
#include <lal/iterators/Q_iterator.hpp>
#include <lal/detail/data_array.hpp>
#include <lal/detail/identity_arrangement.hpp>
 
#define idx(i,j, C) ((i)*(C) + (j))
#define DECIDED_C_GT (upper_bound + 1)
#define DECIDED_C_LE C
 
namespace lal {
namespace detail {
namespace crossings {
 
namespace brute_force {
 
// =============================================================================
// ACTUAL ALGORITHM
// =============================================================================
 
template <bool decide_upper_bound, linarr_type arr_type>
[[nodiscard]] uint64_t compute(
    const graphs::undirected_graph& g,
    const linarr_wrapper<arr_type>& arr,
    uint64_t upper_bound = 0
)
noexcept
{
    uint64_t C = 0;
 
    // iterate over the pairs of edges that will potentially cross
    // using the information given in the linear arrangement
    for (node_t u = 0ull; u < g.get_num_nodes(); ++u) {
        // 'pu' is the position of node 'u'
        const position pu = arr[u];
        const neighbourhood& Nu = g.get_neighbours(*u);
        for (node_t v : Nu) {
            // 'pv' is the position of node 'v'
            const position pv = arr[v];
            if (pu >= pv) { continue; }
 
            // 'u' and 'v' is a pair of connected nodes such that 'u'
            // is "to the left of" 'v' in the linear arrangement 'seq'
 
            // iterate through the positions between 'u' and 'v'
            const position begin = pu + 1;
            const position end = pv - 1;
 
            for (position_t pw = begin; pw <= end; ++pw) {
                // 'w' is the node at position 'pw'
                const node w = arr[pw];
                const neighbourhood& Nw = g.get_neighbours(w);
                for (node_t z : Nw) {
                    const position pz = arr[z];
 
                    // if     arr[w] < arr[z]    then
                    // 'w' and 'z' is a pair of connected nodes such that
                    // 'w' is "to the left of" 'z' in the random seq 'seq'.
                    // Formally: arr[w] < arr[z]
 
                    // Also, by construction: arr[u] < arr[w]
                    C += pw < pz and
                         pu < pw and pw < pv and pv < pz;
 
                    if constexpr (decide_upper_bound) {
                        if (C > upper_bound) { return DECIDED_C_GT; }
                    }
                }
            }
        }
    }
 
    // none of the conditions above were true, so we must have
    // C <= upper_bound
    return C;
}
 
template <bool decide_upper_bound, linarr_type arr_type>
[[nodiscard]] uint64_t inner_compute
(
    const graphs::directed_graph& g,
    position pu, position pv,
    const linarr_wrapper<arr_type>& arr,
    uint64_t C,
    uint64_t upper_bound
)
noexcept
{
    // 'u' and 'v' is a pair of connected nodes such that 'u'
    // is "to the left of" 'v' in the linear arrangement 'seq'
 
    // iterate through the positions between 'u' and 'v'
    const position begin = pu + 1;
    const position end = pv - 1;
 
    for (position_t pw = begin; pw <= end; ++pw) {
        // 'w' is the node at position 'pw'
        const node w = arr[pw];
        const neighbourhood& Nw_out = g.get_out_neighbours(w);
        for (node_t z : Nw_out) {
            const position pz = arr[z];
 
            // if     arr[w] < arr[z]    then
            // 'w' and 'z' is a pair of connected nodes such that
            // 'w' is "to the left of" 'z' in the random seq 'seq'.
            // Formally: arr[w] < arr[z]
 
            // Also, by construction: arr[u] < arr[w]
            C += pw < pz and
                 pu < pw and pw < pv and pv < pz;
 
            if constexpr (decide_upper_bound) {
                if (C > upper_bound) { return DECIDED_C_GT; }
            }
        }
        const neighbourhood& Nw_in = g.get_in_neighbours(w);
        for (node_t z : Nw_in) {
            const position pz = arr[z];
 
            // if     arr[w] < arr[z]    then
            // 'w' and 'z' is a pair of connected nodes such that
            // 'w' is "to the left of" 'z' in the random seq 'seq'.
            // Formally: arr[w] < arr[z]
 
            // Also, by construction: arr[u] < arr[w]
            C += pw < pz and
                 pu < pw and pw < pv and pv < pz;
 
            if constexpr (decide_upper_bound) {
                if (C > upper_bound) { return DECIDED_C_GT; }
            }
        }
    }
 
    // none of the conditions above were true, so we must have
    // C <= upper_bound
    return C;
}
 
template <bool decide_upper_bound, linarr_type arr_type>
uint64_t compute(
    const graphs::directed_graph& g, const linarr_wrapper<arr_type>& arr,
    uint64_t upper_bound
)
noexcept
{
    uint64_t C = 0;
 
    // iterate over the pairs of edges that will potentially cross
    // using the information given in the linear arrangement
    for (node_t u = 0ull; u < g.get_num_nodes(); ++u) {
        // 'pu' is the position of node 'u'
        const position pu = arr[u];
        const neighbourhood& Nu_out = g.get_out_neighbours(*u);
        for (node_t v : Nu_out) {
            // 'pv' is the position of node 'v'
            const position pv = arr[v];
            if (pu >= pv) { continue; }
            // 'u' and 'v' is a pair of connected nodes such that 'u'
            // is "to the left of" 'v' in the linear arrangement 'seq'
 
            C = inner_compute<decide_upper_bound>
                    (g, pu,pv, arr, C, upper_bound);
 
            if constexpr (decide_upper_bound) {
                if (C > upper_bound) { return DECIDED_C_GT; }
            }
        }
        const neighbourhood& Nu_in = g.get_in_neighbours(*u);
        for (node_t v : Nu_in) {
            // 'pv' is the position of node 'v'
            const position pv = arr[v];
            if (pu >= pv) { continue; }
            // 'u' and 'v' is a pair of connected nodes such that 'u'
            // is "to the left of" 'v' in the linear arrangement 'seq'
 
            C = inner_compute<decide_upper_bound>
                    (g, pu,pv, arr, C, upper_bound);
 
            if constexpr (decide_upper_bound) {
                if (C > upper_bound) { return DECIDED_C_GT; }
            }
        }
    }
 
    // none of the conditions above were true, so we must have
    // C <= upper_bound
    return C;
}
 
} // -- namespace brute_force
 
// =============================================================================
// CALLS TO THE ALGORITHM
// =============================================================================
 
// ------------------
// single arrangement
 
template <class graph_t, class arrangement_t>
uint64_t n_C_brute_force(const graph_t& g, const arrangement_t& arr)
noexcept
{
    const uint64_t n = g.get_num_nodes();
 
#if defined DEBUG
    assert(arr.m_arr.size() == 0 or arr.m_arr.size() == n);
#endif
 
    if (n < 4) { return 0; }
 
    return brute_force::compute<false>(g, arr, 0);
}
 
// --------------------
// list of arrangements
 
template <class graph_t>
std::vector<uint64_t> n_C_brute_force
(const graph_t& g, const std::vector<linear_arrangement>& arrs)
noexcept
{
    const uint64_t n = g.get_num_nodes();
 
    std::vector<uint64_t> cs(arrs.size());
    if (n < 4) {
        // fill only when necessary
        std::fill(cs.begin(), cs.end(), 0);
        return cs;
    }
 
    /* compute C for every linear arrangement */
    for (std::size_t i = 0; i < arrs.size(); ++i) {
 
#if defined DEBUG
        // ensure that no linear arrangement is empty
        assert(arrs[i].size() == n);
#endif
 
        // compute C
        cs[i] = brute_force::compute<false>(g, nonident_arr(arrs[i]), 0);
    }
 
    return cs;
}
 
// -----------------------------------------------------------------------------
// DECISION
 
// ------------------
// single arrangement
 
template <class graph_t, class arrangement_t>
uint64_t is_n_C_brute_force_lesseq_than
(const graph_t& g, const arrangement_t& arr, uint64_t upper_bound)
noexcept
{
    const uint64_t n = g.get_num_nodes();
 
#if defined DEBUG
    assert(arr.m_arr.size() == 0 or arr.m_arr.size() == n);
#endif
 
    if (n < 4) { return 0; }
 
    return brute_force::compute<true>(g, arr, upper_bound);
}
 
// --------------------
// list of arrangements
 
template <class graph_t>
std::vector<uint64_t> is_n_C_brute_force_lesseq_than
(const graph_t& g, const std::vector<linear_arrangement>& arrs, uint64_t upper_bound)
noexcept
{
    const uint64_t n = g.get_num_nodes();
 
    std::vector<uint64_t> cs(arrs.size());
    if (n < 4) {
        std::fill(cs.begin(), cs.end(), 0);
        return cs;
    }
 
    /* compute C for every linear arrangement */
    for (std::size_t i = 0; i < arrs.size(); ++i) {
#if defined DEBUG
        // ensure that no linear arrangement is empty
        assert(arrs[i].size() == n);
#endif
 
        // compute C
        cs[i] = brute_force::compute<true>(g, nonident_arr(arrs[i]), upper_bound);
    }
 
    return cs;
}
 
template <class graph_t>
std::vector<uint64_t> is_n_C_brute_force_lesseq_than(
    const graph_t& g,
    const std::vector<linear_arrangement>& arrs,
    const std::vector<uint64_t>& upper_bounds
)
noexcept
{
#if defined DEBUG
    // there must be as many arrangements as upper bounds
    assert(arrs.size() == upper_bounds.size());
#endif
    const uint64_t n = g.get_num_nodes();
 
    std::vector<uint64_t> cs(arrs.size());
    if (n < 4) {
        std::fill(cs.begin(), cs.end(), 0);
        return cs;
    }
 
    /* compute C for every linear arrangement */
    for (std::size_t i = 0; i < arrs.size(); ++i) {
#if defined DEBUG
        // ensure that no linear arrangement is empty
        assert(arrs[i].size() == n);
#endif
 
        // compute C
        cs[i] = brute_force::compute<true>(g, nonident_arr(arrs[i]), upper_bounds[i]);
    }
 
    return cs;
}
 
} // -- namespace crossings
} // -- namespace detail
} // -- namespace lal