dependency_flux.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 <optional>
 
// lal includes
#include <lal/graphs/free_tree.hpp>
#include <lal/iterators/E_iterator.hpp>
#include <lal/detail/identity_arrangement.hpp>
#include <lal/detail/sorting/counting_sort.hpp>
#include <lal/detail/sorting/sorted_vector.hpp>
#include <lal/detail/data_array.hpp>
 
#define max_pos(u,v) (std::max(arr[u], arr[v]))
 
namespace lal {
namespace detail {
 
template <class depflux, class arrangement_t>
void calculate_dependencies_and_span
(
    const graphs::free_tree& t,
    const arrangement_t& arr,
    const std::vector<std::pair<edge_t,uint64_t>>& edge_with_max_pos_at,
    position cur_pos,
    std::vector<depflux>& flux,
    std::vector<edge>& cur_deps
)
noexcept
{
    const node u = arr[position_t{cur_pos}];
 
    if (cur_pos > 0) {
        // copy previous dependencies
        cur_deps = flux[cur_pos - 1].get_dependencies();
    }
 
    // find those edges ending at position 'p' ...
    if (edge_with_max_pos_at[cur_pos].second > 0) {
        const auto [first, last] =
            std::equal_range(
                cur_deps.begin(), cur_deps.end(),
                edge_with_max_pos_at[cur_pos].first, // this ends at position p-1
                [&](const edge_t& e1, const edge_t& e2) -> bool {
                    const auto pos_e1 = max_pos(e1.first, e1.second);
                    const auto pos_e2 = max_pos(e2.first, e2.second);
                    return pos_e1 < pos_e2;
                }
            );
        if (first != cur_deps.end()) {
            cur_deps.erase(first, last);
        }
    }
 
    // add the new dependencies
    for (const node_t v : t.get_neighbours(u)) {
        if (arr[v] > cur_pos) {
            cur_deps.push_back({u,*v});
        }
    }
 
    sorting::sorted_vector<node,true> set_endpoints;
    for (const auto& [v,w] : cur_deps) {
        set_endpoints.insert_sorted(v);
        set_endpoints.insert_sorted(w);
    }
    for (node_t v : set_endpoints) {
        flux[cur_pos].get_left_span() += (arr[v] <= cur_pos);
        flux[cur_pos].get_right_span() += (arr[v] > cur_pos);
    }
}
 
inline uint64_t calculate_weight
(const std::vector<edge>& dependencies, graphs::undirected_graph& ug)
noexcept
{
    if (dependencies.size() <= 1) { return dependencies.size(); }
 
    // build graph
    ug.set_edges(dependencies);
 
    // ------------------------------------------
    // apply the "algorithm", see what happens...
    // step 1. while we can find a leaf
    // step 2. put incident edge in the set of disjoint dependencies
    // step 3. delete edges incident to the other vertex
 
    const auto find_leaf =
    [](const graphs::undirected_graph& g) -> std::optional<node> {
        for (node u = 0; u < g.get_num_nodes(); ++u) {
            if (g.get_degree(u) == 1) { return u; }
        }
        return {};
    };
 
    uint64_t weight = 0;
    // step 1
    while (const auto leaf = find_leaf(ug)) {
        const node u = *leaf;
        const node v = ug.get_neighbours(u)[0];
        // step 2
        ++weight;
        // step 3 -- remove edges incident to the only neighbour of the leaf
        ug.remove_edges_incident_to(v);
    }
 
    return weight;
}
 
/*
 * @brief Calculate fluxes in a linear arrangement.
 * @tparam arrangement_t Type of arrangement.
 * @param t Input free tree.
 * @param arr Input linear arrangement.
 * @returns The set of dependency fluxes in the arrangement.
 */
template <class depflux, class arrangement_t>
std::vector<depflux> compute_flux
(const graphs::free_tree& t, const arrangement_t& arr)
noexcept
{
    const uint64_t n = t.get_num_nodes();
    if (n == 1) { return {}; }
 
    // one edge entering each position
    std::vector<std::pair<edge_t,uint64_t>> edge_with_max_pos_at(n, {{}, 0});
    for (iterators::E_iterator e_it(t); not e_it.end(); e_it.next()) {
        const auto [u,v] = e_it.get_edge_t();
        const position max = max_pos(u, v);
        edge_with_max_pos_at[max].first = {u,v};
        ++edge_with_max_pos_at[max].second;
    }
 
    // the graph (of n vertices) used to calculate the weight
    graphs::undirected_graph ug(n);
 
    // the reusable memory for the sorting algorithm
    sorting::countingsort::memory<edge> mem(n, n);
 
    // declare the result to be returned
    std::vector<depflux> flux(n - 1);
 
    for (position cur_pos = 0; cur_pos < n - 1; ++cur_pos) {
        // current dependencies
        auto& cur_deps = flux[cur_pos].get_dependencies();
 
        // ----------------------
        // calculate dependencies
        calculate_dependencies_and_span<depflux>
        (t, arr, edge_with_max_pos_at, cur_pos, flux, cur_deps);
 
        // -------------------------------------------------
        // calculate the weight of the flux at this position
        // (read the paper for an "algorithm")
        flux[cur_pos].set_weight(calculate_weight(cur_deps, ug));
 
        // sort the dependencies by ending position so that edges
        // can be erased more efficiently in the next iteration
        sorting::counting_sort
        <edge, sorting::non_decreasing_t, false>
        (
            // iterators to the container to be sorted
            cur_deps.begin(), cur_deps.end(),
            // largest key possible + 1
            n,
            // key
            [&](const edge_t& e) -> std::size_t
            { return max_pos(e.first, e.second); },
            // reusable memory
            mem
        );
        mem.reset_count();
    }
 
    return flux;
}
 
} // -- namespace detail
} // -- namespace lal