formal_constraints.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/
 *
 ********************************************************************/
 
#pragma once
 
// lal includes
#include <lal/iterators/E_iterator.hpp>
#include <lal/detail/identity_arrangement.hpp>
#include <lal/graphs/rooted_tree.hpp>
 
namespace lal {
namespace detail {
 
template <detail::linarr_type arr_type>
bool is_root_covered(
    const graphs::rooted_tree& rt,
    const detail::linarr_wrapper<arr_type>& arr
)
noexcept
{
#if defined DEBUG
    assert(rt.is_rooted_tree());
#endif
 
    // case where the linear arrangement is not given
    if (arr.m_arr.size() == 0) {
        const node r = rt.get_root();
        iterators::E_iterator e_it(rt);
        while (not e_it.end()) {
            const auto [s,t] = e_it.yield_edge();
            const bool r_covered_st = s < r and r < t;
            const bool r_covered_ts = t < r and r < s;
            if (r_covered_st or r_covered_ts) { return true; }
        }
        return false;
    }
 
    // the linear arrangement is given
    const position pr = arr[node_t{rt.get_root()}];
 
    iterators::E_iterator e_it(rt);
    while (not e_it.end()) {
        const auto [s,t] = e_it.yield_edge_t();
        const position ps = arr[s];
        const position pt = arr[t];
 
        const bool r_covered_st = ps < pr and pr < pt;
        const bool r_covered_ts = pt < pr and pr < ps;
        if (r_covered_st or r_covered_ts) { return true; }
    }
    return false;
}
 
template <detail::linarr_type arr_type>
bool is_projective(
    const graphs::rooted_tree& rt,
    const detail::linarr_wrapper<arr_type>& arr
)
noexcept
{
#if defined DEBUG
    assert(rt.is_rooted_tree());
#endif
 
    // check for planarity
    // this function already checks that an arrangement must be valid
    if (not is_planar(rt, arr)) { return false; }
    return not is_root_covered(rt, arr);
}
 
} // -- namespace detail
} // -- namespace lal