bipartite_opt_utils.hpp

/*********************************************************************
 *
 * Linear Arrangement Library - A library that implements a collection
 * algorithms for linear arrangments of graphs.
 *
 * Copyright (C) 2019 - 2024
 *
 * 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 (lluis.alemany.puig@upc.edu)
 *         LQMC (Quantitative, Mathematical, and Computational Linguisitcs)
 *         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/
 *
 *     Juan Luis Esteban (esteban@cs.upc.edu)
 *         LOGPROG: Logics and Programming Research Group
 *         Office 110, Omega building
 *         Jordi Girona St 1-3, Campus Nord UPC, 08034 Barcelona.   CATALONIA, SPAIN
 *         Webpage: https://www.cs.upc.edu/~esteban/
 *
 *     Ramon Ferrer i Cancho (rferrericancho@cs.upc.edu)
 *         LQMC (Quantitative, Mathematical, and Computational Linguisitcs)
 *         CQL (Complexity and Quantitative Linguistics Lab)
 *         Office 220, Omega building
 *         Jordi Girona St 1-3, Campus Nord UPC, 08034 Barcelona.   CATALONIA, SPAIN
 *         Webpage: https://cqllab.upc.edu/people/rferrericancho/
 *
 ********************************************************************/
 
#pragma once
 
// lal includes
#include <lal/linear_arrangement.hpp>
#include <lal/detail/array.hpp>
#include <lal/iterators/E_iterator.hpp>
#include <lal/detail/graphs/size_subtrees.hpp>
#include <lal/detail/sorting/counting_sort.hpp>
#include <lal/detail/properties/tree_centroid.hpp>
 
namespace lal {
namespace detail {
 
namespace bipartite_opt_utils {
 
template <
    bool make_arrangement,
    sorting::sort_type type,
    class graph_t,
    class bipartite_coloring_t
>
[[nodiscard]] std::conditional_t<
    make_arrangement,
    std::pair<uint64_t, linear_arrangement>,
    uint64_t
>
optimal_bipartite_arrangement_AEF
(const graph_t& g, const bipartite_coloring_t& c)
noexcept
{
    static_assert(std::is_base_of_v<graphs::graph, graph_t>);
 
    const auto n = g.get_num_nodes();
 
    // annoying corner case
    if (n == 1) {
        if constexpr (make_arrangement) {
            return {0, linear_arrangement::identity(n)};
        }
        else {
            return 0;
        }
    }
 
    array<node> vertices_color_1(n - 1);
    std::size_t size_1 = 0;
    array<node> vertices_color_2(n - 1);
    std::size_t size_2 = 0;
 
    {
    const auto first_color = c[0];
    for (node u = 0; u < n; ++u) {
        if (c[u] == first_color) {
            vertices_color_1[size_1++] = u;
        }
        else {
            vertices_color_2[size_2++] = u;
        }
    }
 
    const auto sort_nodes =
    [&](array<node>& nodes, std::size_t s) {
        sorting::counting_sort
            <node, type>
            (
                nodes.begin(), nodes.begin() + s,
                n - 1,
                s,
                [&](const node u) -> std::size_t {
                    // in directed graphs, this function returns the sum of the
                    // in-degree plus the out-degree of the vertex.
                    return g.get_degree(u);
                }
            );
    };
    sort_nodes(vertices_color_1, size_1);
    sort_nodes(vertices_color_2, size_2);
    }
 
    uint64_t D = 0;
    linear_arrangement arr;
 
    if constexpr (make_arrangement) {
        arr.resize(n);
    }
 
    position p = 0;
    for (std::size_t i = size_1 - 1; i > 0; --i) {
        const node u = vertices_color_1[i];
        if constexpr (make_arrangement) {
            arr.assign(u, p);
            ++p;
        }
        D += (n - p)*g.get_degree(u);
    }
 
    {
    const node u = vertices_color_1[0];
    if constexpr (make_arrangement) {
        arr.assign(vertices_color_1[0], p);
        ++p;
    }
    D += (n - p)*g.get_degree(u);
    }
 
    for (std::size_t i = 0; i < size_2; ++i) {
        const node u = vertices_color_2[i];
        if constexpr (make_arrangement) {
            arr.assign(u, p);
            ++p;
        }
        D -= (n - p)*g.get_degree(u);
    }
 
    if constexpr (make_arrangement) {
        return {D, std::move(arr)};
    }
    else {
        return D;
    }
}
 
} // -- namespcae bipartite_opt_utils
} // -- namespace detail
} // -- namespace lal