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
 
// C++ includes
#if defined DEBUG
#include <cassert>
#endif
#include <numeric>
 
// lal includes
#include <lal/graphs/rooted_tree.hpp>
#include <lal/linarr/C.hpp>
#include <lal/iterators/E_iterator.hpp>
#include <lal/detail/data_array.hpp>
#include <lal/detail/identity_arrangement.hpp>
 
namespace lal {
namespace linarr {
 
inline
bool is_permutation(const linear_arrangement& arr = {}) noexcept {
    // identity arrangement is always a permutation                                                      
    if (arr.size() == 0) { return true; }
    // an arrangement of a single element is a permutation                                               
    // if its only element is within range                                                               
    if (arr.size() == 1) {
        return arr[lal::position_t{0ull}] == 0;                                                          
    }
    // ensure that no position has been used twice
    detail::data_array<char> d(arr.size(), 0);                                                                                                                                                                     
    for (node_t u = 0ull; u < arr.size(); ++u) {                                                         
        const position p = arr[u];
        // ensure all elements are within range                                                          
        if (p >= arr.size()) { return false; }
        // if a value already exists, this is not a permutation                                          
        if (d[p] > 0) { return false; }                                                                  
        d[p] += 1;                                                                                       
    }
    return true;
}
 
template <class graph_t>
bool is_arrangement(const graph_t& g, const linear_arrangement& arr) noexcept
{
    if constexpr (std::is_base_of_v<graph_t, graphs::tree>) {
#if defined DEBUG
        assert(g.is_tree());
#endif
    }
 
    // identity arrangement is always a permutation
    if (arr.size() == 0) { return true; }
    // if sizes differ then the arrangement is not a permutation
    if (g.get_num_nodes() != arr.size()) { return false; }
    // ensure that the input arrangement is a permutation
    if (not is_permutation(arr)) { return false; }
    // the largest number must be exactly one less than the size
    const position max_pos =
        *std::max_element(arr.begin_direct(), arr.end_direct());
 
    return max_pos == arr.size() - 1;
}
 
template <class graph_t>
bool is_planar(const graph_t& g, const linear_arrangement& arr = {}) noexcept {
#if defined DEBUG
    assert(is_arrangement(g, arr));
#endif
 
    return is_num_crossings_lesseq_than(g, arr, 0) <= 0;
}
 
bool is_root_covered(const graphs::rooted_tree& rt, const linear_arrangement& arr)
noexcept;
 
inline
bool is_projective(const graphs::rooted_tree& rt, const linear_arrangement& 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 linarr
} // -- namespace lal