D_rla.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
 
// lal includes
#include <lal/numeric/rational.hpp>
#include <lal/graphs/undirected_graph.hpp>
#include <lal/graphs/free_tree.hpp>
#include <lal/graphs/rooted_tree.hpp>
 
namespace lal {
namespace properties {
 
// D: sum of length of edges
 
/* ---------------------------- */
/*  EXPECTATION OF D: E_rla[D]  */
/* (unconstrained arrangements) */
 
inline
numeric::rational exp_sum_edge_lengths_rational(const graphs::undirected_graph& g)
noexcept {
    return numeric::rational((g.get_num_nodes() + 1)*g.get_num_edges(), 3);
}
 
inline
double exp_sum_edge_lengths(const graphs::undirected_graph& g) noexcept {
    return exp_sum_edge_lengths_rational(g).to_double();
}
 
inline
numeric::rational exp_sum_edge_lengths_rational(const graphs::free_tree& t)
noexcept {
#if defined DEBUG
    assert(t.is_tree());
#endif
    const uint64_t n = t.get_num_nodes();
    return numeric::rational(n*n - 1, 3);
}
 
inline
double exp_sum_edge_lengths(const graphs::free_tree& t) noexcept {
#if defined DEBUG
    assert(t.is_tree());
#endif
    return exp_sum_edge_lengths_rational(t).to_double();
}
 
inline
numeric::rational exp_sum_edge_lengths_rational(const graphs::rooted_tree& t)
noexcept {
#if defined DEBUG
    assert(t.is_rooted_tree());
#endif
    const uint64_t n = t.get_num_nodes();
    return numeric::rational(n*n - 1, 3);
}
 
inline
double exp_sum_edge_lengths(const graphs::rooted_tree& t) noexcept {
#if defined DEBUG
    assert(t.is_rooted_tree());
#endif
    return exp_sum_edge_lengths_rational(t).to_double();
}
 
 
/* ------------------------- */
/* EXPECTATION OF D: E_pr[D] */
/* (projective arrangements) */
 
numeric::rational exp_sum_edge_lengths_projective_rational
(const graphs::rooted_tree& rt) noexcept;
 
inline
double exp_sum_edge_lengths_projective(const graphs::rooted_tree& rt) noexcept {
    return exp_sum_edge_lengths_projective_rational(rt).to_double();
}
 
 
/* ------------------------- */
/* EXPECTATION OF D: E_pl[D] */
/*   (planar arrangements)   */
 
numeric::rational exp_sum_edge_lengths_planar_rational
(const graphs::free_tree& t) noexcept;
inline
numeric::rational exp_sum_edge_lengths_planar_rational
(const graphs::rooted_tree& rt) noexcept
{ return exp_sum_edge_lengths_planar_rational(rt.to_undirected()); }
 
inline
double exp_sum_edge_lengths_planar
(const graphs::free_tree& t) noexcept
{ return exp_sum_edge_lengths_planar_rational(t).to_double(); }
inline
double exp_sum_edge_lengths_planar
(const graphs::rooted_tree& rt) noexcept
{ return exp_sum_edge_lengths_planar_rational(rt).to_double(); }
 
 
/* ---------------------------- */
/*    VARIANCE OF D: V_rla[D]   */
/* (unconstrained arrangements) */
 
numeric::rational var_sum_edge_lengths_rational(const graphs::undirected_graph& g)
noexcept;
inline
double var_sum_edge_lengths(const graphs::undirected_graph& g) noexcept
{ return var_sum_edge_lengths_rational(g).to_double(); }
 
} // -- namespace properties
} // -- namespace lal