tree_isomorphism.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 <algorithm>
#include <cinttypes>
#if defined DEBUG
#include <cassert>
#endif
 
// lal includes
#include <lal/graphs/rooted_tree.hpp>
#include <lal/detail/macros/basic_convert.hpp>
#include <lal/detail/data_array.hpp>
 
namespace lal {
namespace detail {
 
template <
    class tree_t,
    std::enable_if_t< std::is_base_of_v<graphs::tree, tree_t>, bool> = true
>
char fast_non_iso(const tree_t& t1, const tree_t& t2) noexcept
{
    // check number of nodes
    if (t1.get_num_nodes() != t2.get_num_nodes()) { return 1; }
 
    const uint64_t n = t1.get_num_nodes();
 
    // trees ARE isomorphic
    if (n <= 2) { return 0; }
 
    uint64_t nL_t1 = 0; // number of leaves of t1
    uint64_t nL_t2 = 0; // number of leaves of t2
    uint64_t k2_t1 = 0; // sum of squared degrees of t1
    uint64_t k2_t2 = 0; // sum of squared degrees of t2
    uint64_t maxdeg_t1 = 0; // max degree of t1
    uint64_t maxdeg_t2 = 0; // max degree of t2
    for (node u = 0; u < n; ++u) {
        const uint64_t ku1 = to_uint64(t1.get_degree(u));
        const uint64_t ku2 = to_uint64(t2.get_degree(u));
 
        nL_t1 += t1.get_degree(u) == 1;
        nL_t2 += t2.get_degree(u) == 1;
        k2_t1 += ku1*ku1;
        k2_t2 += ku2*ku2;
        maxdeg_t1 = (maxdeg_t1 < ku1 ? ku1 : maxdeg_t1);
        maxdeg_t2 = (maxdeg_t2 < ku2 ? ku2 : maxdeg_t2);
    }
 
    // check number of leaves
    if (nL_t1 != nL_t2) { return 1; }
    // check maximum degree
    if (maxdeg_t1 != maxdeg_t2) { return 1; }
    // check sum of squared degrees
    if (k2_t1 != k2_t2) { return 1; }
 
    // trees MIGHT BE isomorphic
    return 2;
}
 
inline
void assign_name_and_keep(
    const graphs::rooted_tree& t, node u,
    std::size_t idx,
    std::string * const aux_memory_for_names,
    std::string * const keep_name_of
)
noexcept
{
    if (t.get_out_degree(u) == 0) {
        keep_name_of[u] = "10";
        return;
    }
 
    // make childrens' names
    const std::size_t begin_idx = idx;
    for (node v : t.get_out_neighbours(u)) {
        // make the name for v
        assign_name_and_keep(t,v, idx+1, aux_memory_for_names, keep_name_of);
 
        aux_memory_for_names[idx] = keep_name_of[v];
        ++idx;
    }
    std::sort(&aux_memory_for_names[begin_idx], &aux_memory_for_names[idx]);
 
    // join the names in a single string to make the name of vertex 'v'
    std::string name = "1";
    for (std::size_t j = begin_idx; j < idx; ++j) {
        name += aux_memory_for_names[j];
    }
    name += "0";
    keep_name_of[u] = name;
}
 
inline
std::string assign_name
(const graphs::rooted_tree& t, node u, std::string * const names, std::size_t idx)
noexcept
{
    if (t.get_out_degree(u) == 0) {
        return std::string("10");
    }
 
    // make childrens' names
    const std::size_t begin_idx = idx;
    for (node v : t.get_out_neighbours(u)) {
        // make the name for v
        names[idx] = assign_name(t,v, names, idx+1);
        ++idx;
    }
    std::sort(&names[begin_idx], &names[idx]);
 
    // join the names in a single string to make the name of vertex 'v'
    std::string name = "1";
    for (std::size_t j = begin_idx; j < idx; ++j) {
        name += names[j];
    }
    name += "0";
 
    return name;
}
 
inline
bool are_full_trees_isomorphic
(const graphs::rooted_tree& t1, const graphs::rooted_tree& t2)
noexcept
{
    const auto discard = detail::fast_non_iso(t1,t2);
    if (discard == 0) { return true; }
    if (discard == 1) { return false; }
 
    data_array<std::string> names(t1.get_num_nodes());
    const std::string name_r1 = assign_name(t1, t1.get_root(), names.begin(), 0);
    const std::string name_r2 = assign_name(t2, t2.get_root(), names.begin(), 0);
    return name_r1 == name_r2;
}
 
} // -- namespace detail
} // -- namespace lal