algorithms_crossings.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
#include <vector>
 
// lal includes
#include <lal/linear_arrangement.hpp>
#include <lal/graphs/graph.hpp>
#include <lal/graphs/directed_graph.hpp>
#include <lal/graphs/undirected_graph.hpp>
 
namespace lal {
namespace detail {
 
/*
 * This file is a summary of the functions that implement the different
 * algorithms to calculate the number of edge crossings.
 */
 
template <class graph_t>
uint64_t n_C_brute_force
(const graph_t& g, const linear_arrangement& arr)
noexcept;
 
template <class graph_t>
std::vector<uint64_t> n_C_brute_force
(const graph_t& g, const std::vector<linear_arrangement>& arrs)
noexcept;
 
template <class graph_t>
uint64_t is_n_C_brute_force_lesseq_than(
    const graph_t& g,
    const linear_arrangement& arr,
    uint64_t upper_bound
) noexcept;
 
template <class graph_t>
std::vector<uint64_t> is_n_C_brute_force_lesseq_than(
    const graph_t& g,
    const std::vector<linear_arrangement>& arrs,
    uint64_t upper_bound
) noexcept;
 
template <class graph_t>
std::vector<uint64_t> is_n_C_brute_force_lesseq_than(
    const graph_t& g,
    const std::vector<linear_arrangement>& arrs,
    const std::vector<uint64_t>& upper_bounds
) noexcept;
 
// -----------------------------------------------------------------------------
 
template <class graph_t>
uint64_t n_C_dynamic_programming
(const graph_t& g, const linear_arrangement& arr)
noexcept;
 
template <class graph_t>
std::vector<uint64_t> n_C_dynamic_programming(
    const graph_t& g,
    const std::vector<linear_arrangement>& arrs
) noexcept;
 
template <class graph_t>
uint64_t is_n_C_dynamic_programming_lesseq_than(
    const graph_t& g,
    const linear_arrangement& arr,
    uint64_t upper_bound
) noexcept;
 
template <class graph_t>
std::vector<uint64_t> is_n_C_dynamic_programming_lesseq_than(
    const graph_t& g,
    const std::vector<linear_arrangement>& arrs,
    uint64_t upper_bound
) noexcept;
 
template <class graph_t>
std::vector<uint64_t> is_n_C_dynamic_programming_lesseq_than(
    const graph_t& g,
    const std::vector<linear_arrangement>& arrs,
    const std::vector<uint64_t>& upper_bounds
) noexcept;
 
// -----------------------------------------------------------------------------
 
template <class graph_t>
uint64_t n_C_ladder
(const graph_t& g, const linear_arrangement& arr)
noexcept;
 
template <class graph_t>
std::vector<uint64_t> n_C_ladder(
    const graph_t& g,
    const std::vector<linear_arrangement>& arrs
) noexcept;
 
template <class graph_t>
uint64_t is_n_C_ladder_lesseq_than(
    const graph_t& g,
    const linear_arrangement& arr,
    uint64_t upper_bound
) noexcept;
 
template <class graph_t>
std::vector<uint64_t> is_n_C_ladder_lesseq_than(
    const graph_t& g,
    const std::vector<linear_arrangement>& arrs,
    uint64_t upper_bound
) noexcept;
 
template <class graph_t>
std::vector<uint64_t> is_n_C_ladder_lesseq_than(
    const graph_t& g,
    const std::vector<linear_arrangement>& arrs,
    const std::vector<uint64_t>& upper_bounds
) noexcept;
 
// -----------------------------------------------------------------------------
 
template <class graph_t>
uint64_t n_C_stack_based
(const graph_t& g, const linear_arrangement& arr)
noexcept;
 
template <class graph_t>
std::vector<uint64_t> n_C_stack_based(
    const graph_t& g,
    const std::vector<linear_arrangement>& arrs
) noexcept;
 
template <class graph_t>
uint64_t is_n_C_stack_based_lesseq_than(
    const graph_t& g,
    const linear_arrangement& arr,
    uint64_t upper_bound
) noexcept;
 
template <class graph_t>
std::vector<uint64_t> is_n_C_stack_based_lesseq_than(
    const graph_t& g,
    const std::vector<linear_arrangement>& arrs,
    uint64_t upper_bound
) noexcept;
 
template <class graph_t>
std::vector<uint64_t> is_n_C_stack_based_lesseq_than(
    const graph_t& g,
    const std::vector<linear_arrangement>& arrs,
    const std::vector<uint64_t>& upper_bounds
) noexcept;
 
} // -- namespace detail
} // -- namespace lal