necessary_conditions.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/
 *
 *     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/detail/linarr/level_signature.hpp>
 
namespace lal {
namespace detail {
 
template <class graph_t, level_signature_type t>
[[nodiscard]] inline bool is_level_signature_nonincreasing
(
    const graph_t& g,
    const level_signature<t>& levels,
    const linear_arrangement& arr
)
noexcept
{
    const auto n = g.get_num_nodes();
    if constexpr (t == level_signature_type::per_position) {
        for (position_t p = 0ull; p < n - 1ull; ++p) {
            if (levels[p] < levels[p + 1ull]) {
                return false;
            }
        }
    }
    else {
        for (position_t p = 0ull; p < n - 1ull; ++p) {
            const node_t u = (arr.size() == 0 ? *p : arr[p]);
            const node_t v = (arr.size() == 0 ? *p + 1 : arr[p + 1ull]);
            if (levels[u] < levels[v]) {
                return false;
            }
        }
    }
    return true;
}
 
template <class graph_t, level_signature_type t>
[[nodiscard]] inline bool no_two_adjacent_vertices_have_same_level
(
    const graph_t& g,
    const level_signature<t>& levels,
    const linear_arrangement& arr
)
noexcept
{
    if constexpr (t == level_signature_type::per_position) {
        for (iterators::E_iterator it(g); not it.end(); it.next()) {
            const auto [u, v] = it.yield_edge_t();
            const position_t pu = (arr.size() == 0 ? *u : arr[u]);
            const position_t pv = (arr.size() == 0 ? *v : arr[v]);
            if (levels[pu] == levels[pv]) {
                return false;
            }
        }
    }
    else {
        for (iterators::E_iterator it(g); not it.end(); it.next()) {
            const auto [u, v] = it.yield_edge_t();
            if (levels[u] == levels[v]) {
                return false;
            }
        }
    }
    return true;
}
 
template <class graph_t, level_signature_type t>
[[nodiscard]] inline bool no_vertex_in_antenna_is_thistle
(
    const graph_t& g,
    const std::vector<properties::branchless_path>& bps,
    const level_signature<t>& levels,
    const linear_arrangement& arr
)
noexcept
{
 
    for (const properties::branchless_path& bp : bps) {
        if (not bp.is_antenna(g)) { continue; }
 
        const auto& seq = bp.get_vertex_sequence();
        for (std::size_t i = 1; i < seq.size() - 1; ++i) {
            const node_t u = seq[i];
#if defined DEBUG
            assert(g.get_degree(*u) == 2);
#endif
 
            if (is_thistle_vertex(g, levels, u, arr)) { return false; }
        }
    }
    return true;
}
 
template <class graph_t, level_signature_type t>
[[nodiscard]] inline bool at_most_one_thistle_in_bridges
(
    const graph_t& g,
    const std::vector<properties::branchless_path>& bps,
    const level_signature<t>& levels,
    const linear_arrangement& arr
)
noexcept
{
 
    for (const properties::branchless_path& bp : bps) {
        if (bp.is_antenna(g)) { continue; }
 
        uint64_t num_thistles = 0;
        const auto& seq = bp.get_vertex_sequence();
        for (std::size_t i = 1; i < seq.size() - 1; ++i) {
            const node_t u = seq[i];
#if defined DEBUG
            assert(g.get_degree(*u) == 2);
#endif
 
            num_thistles +=
                (num_thistles == 2 ? 0ull : is_thistle_vertex(g, levels, u, arr));
        }
        if (num_thistles > 1) {
            return false;
        }
    }
    return true;
}
 
} // -- namespace detail
} // -- namespace lal