formal_constraints.hpp

/*********************************************************************
 *
 *  Linear Arrangement Library - A library that implements a collection
 *  algorithms for linear arrangments of graphs.
 *
 *  Copyright (C) 2019 - 2021
 *
 *  This file is part of Linear Arrangement Library. To see the full code
 *  visit the webpage:
 *      https://github.com/lluisalemanypuig/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/internal/data_array.hpp>
 
namespace lal {
namespace linarr {
 
inline bool is_permutation(const linear_arrangement& arr = {}) noexcept {
    if (arr.size() == 0) { return true; }
    // ensure that no position has been used twice
    internal::data_array<position> d(arr.size(), 0);
    for (const position p : arr) {
        if (p >= arr.size()) { return false; }
        if (d[p] > 0) { return false; }
        d[p] += 1;
    }
    return true;
}
 
template<class G>
inline bool is_arrangement(const G& g, const linear_arrangement& arr) noexcept
{
    if constexpr (std::is_base_of_v<G, 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(), arr.end());
    return max_pos == arr.size() - 1;
}
 
template<class G>
inline bool is_planar(const G& g, const linear_arrangement& arr = {}) noexcept {
#if defined DEBUG
    assert(is_arrangement(g, arr));
#endif
 
    const uint32_t invalid = g.get_num_edges()*g.get_num_edges() + 1;
    return is_num_crossings_lesseq_than(g, arr, 0) < invalid;
}
 
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; }
 
    if (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.get_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 false; }
            e_it.next();
        }
        return true;
    }
 
    const node r = rt.get_root();
    iterators::E_iterator e_it(rt);
    while (not e_it.end()) {
        const auto [s,t] = e_it.get_edge();
        const bool r_covered_st = arr[s] < arr[r] and arr[r] < arr[t];
        const bool r_covered_ts = arr[t] < arr[r] and arr[r] < arr[s];
        if (r_covered_st or r_covered_ts) { return false; }
        e_it.next();
    }
    return true;
}
 
} // -- namespace linarr
} // -- namespace lal