From 4421ca203f3f8b32925099c38779d1eb55f2214b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jan=20Uhl=C3=ADk?= <jan@uhlik.me>
Date: Thu, 29 Mar 2018 21:02:24 +0200
Subject: [PATCH] Add MM algorithm.
---
alib2graph_algo/src/shortest_path/MM.cpp | 92 ++++++++
alib2graph_algo/src/shortest_path/MM.hpp | 271 +++++++++++++++++++++++
2 files changed, 363 insertions(+)
create mode 100644 alib2graph_algo/src/shortest_path/MM.cpp
create mode 100644 alib2graph_algo/src/shortest_path/MM.hpp
diff --git a/alib2graph_algo/src/shortest_path/MM.cpp b/alib2graph_algo/src/shortest_path/MM.cpp
new file mode 100644
index 0000000000..c6c04f6636
--- /dev/null
+++ b/alib2graph_algo/src/shortest_path/MM.cpp
@@ -0,0 +1,92 @@
+// MM.cpp
+//
+// Created on: 02. 02. 2018
+// Author: Jan Uhlik
+// Modified by:
+//
+// Copyright (c) 2017 Czech Technical University in Prague | Faculty of Information Technology. All rights reserved.
+// Git repository: https://gitlab.fit.cvut.cz/algorithms-library-toolkit/automata-library
+
+#include "MM.hpp"
+
+#include <registration/AlgoRegistration.hpp>
+
+namespace {
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+auto MM1 = registration::AbstractRegister<shortest_path::MM,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedUndirectedGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::MM::findPathBidirectionalRegistration);
+
+auto MM2 = registration::AbstractRegister<shortest_path::MM,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedUndirectedMultiGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::MM::findPathBidirectionalRegistration);
+
+auto MM3 = registration::AbstractRegister<shortest_path::MM,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedDirectedGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::MM::findPathBidirectionalRegistration);
+
+auto MM4 = registration::AbstractRegister<shortest_path::MM,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedDirectedMultiGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::MM::findPathBidirectionalRegistration);
+
+auto MM5 = registration::AbstractRegister<shortest_path::MM,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedMixedGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::MM::findPathBidirectionalRegistration);
+
+auto MM6 = registration::AbstractRegister<shortest_path::MM,
+ ext::pair<ext::vector<DefaultNodeType>, DefaultWeightType>,
+ const graph::WeightedMixedMultiGraph<> &,
+ const DefaultNodeType &,
+ const DefaultNodeType &,
+ std::function<DefaultWeightType(const DefaultNodeType &,
+ const DefaultNodeType &)> >(
+ shortest_path::MM::findPathBidirectionalRegistration);
+
+auto MMGrid1 = registration::AbstractRegister<shortest_path::MM,
+ ext::pair<ext::vector<DefaultSquareGridNodeType>, DefaultWeightType>,
+ const grid::WeightedSquareGrid4<> &,
+ const DefaultSquareGridNodeType &,
+ const DefaultSquareGridNodeType &,
+ std::function<DefaultWeightType(const DefaultSquareGridNodeType &,
+ const DefaultSquareGridNodeType &)> >(
+ shortest_path::MM::findPathBidirectionalRegistration);
+
+auto MMGrid2 = registration::AbstractRegister<shortest_path::MM,
+ ext::pair<ext::vector<DefaultSquareGridNodeType>, DefaultWeightType>,
+ const grid::WeightedSquareGrid8<> &,
+ const DefaultSquareGridNodeType &,
+ const DefaultSquareGridNodeType &,
+ std::function<DefaultWeightType(const DefaultSquareGridNodeType &,
+ const DefaultSquareGridNodeType &)> >(
+ shortest_path::MM::findPathBidirectionalRegistration);
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+}
diff --git a/alib2graph_algo/src/shortest_path/MM.hpp b/alib2graph_algo/src/shortest_path/MM.hpp
new file mode 100644
index 0000000000..c2bd18ba42
--- /dev/null
+++ b/alib2graph_algo/src/shortest_path/MM.hpp
@@ -0,0 +1,271 @@
+// MM.hpp
+//
+// Created on: 02. 02. 2018
+// Author: Jan Uhlik
+// Modified by:
+//
+// Copyright (c) 2017 Czech Technical University in Prague | Faculty of Information Technology. All rights reserved.
+// Git repository: https://gitlab.fit.cvut.cz/algorithms-library-toolkit/automata-library
+
+#ifndef ALIB2_MM_HPP
+#define ALIB2_MM_HPP
+
+#include <alib/vector>
+#include <alib/map>
+#include <alib/set>
+#include <alib/tuple>
+#include <functional>
+#include <alib/algorithm>
+
+#include <common/ReconstructPath.hpp>
+#include <common/SupportFunction.hpp>
+
+namespace shortest_path {
+
+class MM {
+// ---------------------------------------------------------------------------------------------------------------------
+
+ public:
+
+ /// Find the shortest path using AStar algorithm with MM optimalization from the \p start node to the \p goal node in the \p graph.
+ /// This algorithm is run in both direction, from \p start and also from \p goal.
+ ///
+ /// Whenever node is opened, \p f_user is called with two parameters (the opened node and value of currently shortest path).
+ ///
+ /// The heuristic function must be admissible and monotone.
+ ///
+ /// \param graph to explore.
+ /// \param start initial node.
+ /// \param goal final node.
+ /// \param f_heuristic_forward front-to-end (node->goal) heuristic function which accept node and return edge_type::weight_type
+ /// \param f_heuristic_backward front-to-end (node->start) heuristic function which accept node and return edge_type::weight_type
+ /// \param f_user function which is called for every opened node with value of currently shortest path.
+ ///
+ /// \returns pair where first := shortest path := distance of path, if there is no such path vector is empty and distance std::numeric_limits<edge_type:weight_type>::max()
+ ///
+ /// \note TEdge of \p graph must follow graph::edge::WeightedEdge interface
+ /// \sa graph::edge_type::WeightedEdge
+ ///
+ /// \throws std::out_of_range if \p graph contains an edge with a negative weight
+ ///
+ template<
+ typename TGraph,
+ typename TNode,
+ typename F1 = std::function<typename TGraph::edge_type::weight_type(const TNode &)>,
+ typename F2 = std::function<typename TGraph::edge_type::weight_type(const TNode &)>,
+ typename F3 = std::function<void(const TNode &, const typename TGraph::edge_type::weight_type &)>>
+ static
+ ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+ findPathBidirectional(const TGraph &graph,
+ const TNode &start,
+ const TNode &goal,
+ F1 f_heuristic_forward,
+ F2 f_heuristic_backward,
+ F3 f_user = [](const TNode &,
+ const typename TGraph::edge_type::weight_type &) {});
+
+ template<
+ typename TGraph,
+ typename TNode,
+ typename F1 = std::function<typename TGraph::edge_type::weight_type(const TNode &, const TNode &)>
+ >
+ static
+ ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+ findPathBidirectionalRegistration(const TGraph &graph,
+ const TNode &start,
+ const TNode &goal,
+ F1 f_heuristic) {
+ return findPathBidirectional(graph, start, goal,
+ [&](const TNode &n) { return f_heuristic(goal, n); },
+ [&](const TNode &n) { return f_heuristic(start, n); });
+
+ }
+
+
+// =====================================================================================================================
+
+ private:
+
+ template<typename TNode, typename TWeight>
+ struct Data {
+ ext::set<ext::tuple<TWeight, TWeight, TNode>> queue; // priority queue
+
+ ext::set<ext::pair<TWeight, TNode>> f_set; // F score of currently OPEN nodes
+ ext::map<TNode, TWeight> f_map; // F score
+
+ ext::set<ext::pair<TWeight, TNode>> g_set; // G score of currently OPEN nodes
+ ext::map<TNode, TWeight> g_map; // G score
+
+ ext::map<TNode, TNode> p; // parents
+ };
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+ template<typename FSuccEdge, typename TNode, typename TWeight, typename F1, typename F2, typename F3>
+ static void relaxation(FSuccEdge successor_edges,
+ Data<TNode, TWeight> &data,
+ F1 f_heuristic,
+ F2 f_user,
+ F3 f_update);
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+ template<typename TNode, typename TWeight, typename F>
+ inline static void init(MM::Data<TNode, TWeight> &data, const TNode &start, F f_heuristic);
+
+
+
+// ---------------------------------------------------------------------------------------------------------------------
+};
+
+// =====================================================================================================================
+
+template<typename TGraph, typename TNode, typename F1, typename F2, typename F3>
+ext::pair<ext::vector<TNode>, typename TGraph::edge_type::weight_type>
+MM::findPathBidirectional(const TGraph &graph,
+ const TNode &start,
+ const TNode &goal,
+ F1 f_heuristic_forward,
+ F2 f_heuristic_backward,
+ F3 f_user) {
+
+ using weight_type = typename TGraph::edge_type::weight_type;
+
+ weight_type eps = common::SupportFunction::getMinEdgeValue(graph); // Smallest value of the weight in graph
+
+ weight_type p = std::numeric_limits<weight_type>::max(); // Currently best path weight
+ ext::vector<TNode> intersection_nodes; // Last one is currently best intersection node
+ Data<TNode, weight_type> forward_data, backward_data;
+
+ // Init forward search
+ init(forward_data, start, f_heuristic_forward);
+ auto f_forward_update = [&](const auto &s) -> void {
+ if (backward_data.g_map.find(s) != backward_data.g_map.end()) {
+ if (forward_data.g_map.at(s) + backward_data.g_map.at(s) < p) {
+ p = forward_data.g_map.at(s) + backward_data.g_map.at(s);
+ intersection_nodes.push_back(s);
+ }
+ }
+ };
+
+ // Init backward search
+ init(backward_data, goal, f_heuristic_backward);
+ auto f_backward_update = [&](const auto &s) -> void {
+ if (forward_data.g_map.find(s) != forward_data.g_map.end()) {
+ if (backward_data.g_map.at(s) + forward_data.g_map.at(s) < p) {
+ p = backward_data.g_map.at(s) + forward_data.g_map.at(s);
+ intersection_nodes.push_back(s);
+ }
+ }
+ };
+
+ while (!forward_data.queue.empty() && !backward_data.queue.empty()) {
+ // Check whether can stop searching
+ if (ext::max(std::min(std::get<0>(*forward_data.queue.begin()),
+ std::get<0>(*backward_data.queue.begin())),
+ forward_data.f_set.begin()->first,
+ backward_data.f_set.begin()->first,
+ forward_data.g_set.begin()->first + backward_data.g_set.begin()->first + eps)
+ >= p) {
+ return common::ReconstructPath::reconstructWeightedPath(forward_data.p,
+ backward_data.p,
+ forward_data.g_map,
+ backward_data.g_map,
+ start,
+ goal,
+ intersection_nodes.back());
+ }
+
+ // Expand the lower value
+ if (std::get<0>(*forward_data.queue.begin()) < std::get<0>(*backward_data.queue.begin())) {
+ // Forward search
+ relaxation([&](const auto &node) -> auto { return graph.successorEdges(node); },
+ forward_data,
+ f_heuristic_forward,
+ f_user,
+ f_forward_update);
+ } else {
+ // Backward search
+ relaxation([&](const auto &node) -> auto { return graph.predecessorEdges(node); },
+ backward_data,
+ f_heuristic_backward,
+ f_user,
+ f_backward_update);
+ }
+ }
+
+ return ext::make_pair(ext::vector<TNode>(), p);
+}
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+template<typename FSuccEdge, typename TNode, typename TWeight, typename F1, typename F2, typename F3>
+void MM::relaxation(FSuccEdge successor_edges,
+ MM::Data<TNode, TWeight> &data,
+ F1 f_heuristic,
+ F2 f_user,
+ F3 f_update) {
+ TNode n = std::get<2>(*data.queue.begin());
+ data.queue.erase(data.queue.begin()); // erase from priority queue
+ data.f_set.erase(data.f_set.find(ext::make_pair(data.f_map[n], n))); // erase from f score ordered array
+ data.g_set.erase(data.g_set.find(ext::make_pair(data.g_map[n], n))); // erase from g score ordered array
+
+ // Run user's function
+ f_user(n, data.g_map[n]);
+
+ for (const auto &s_edge: successor_edges(n)) {
+ const TNode &s = common::SupportFunction::other(s_edge, n); // successor
+
+ // Check for negative edge
+ if (s_edge.weight() < 0) {
+ throw std::out_of_range("MM: Detect negative weight on edge in graph.");
+ }
+
+ // Calculate new G score and F score
+ TWeight gscore = data.g_map.at(n) + s_edge.weight();
+
+ // Search if the node s was already visited
+ auto search_g = data.g_map.find(s);
+
+ // If not or the G score can be improve do relaxation
+ if (search_g == data.g_map.end() || data.g_map.at(s) > gscore) {
+ // Search if the node s is in OPEN
+ auto search_q = data.queue.find(ext::make_tuple(std::max(data.f_map[s], 2 * data.g_map[s]), data.g_map[s], s));
+
+ if (search_q != data.queue.end()) {
+ // Erase node from priority queue
+ data.queue.erase(search_q);
+ data.g_set.erase(data.g_set.find(ext::make_pair(data.g_map[s], s)));
+ data.f_set.erase(data.f_set.find(ext::make_pair(data.f_map[s], s)));
+ }
+
+ data.g_map[s] = gscore;
+ data.g_set.insert(ext::make_pair(data.g_map[s], s));
+ data.f_map[s] = gscore + f_heuristic(s);
+ data.f_set.insert(ext::make_pair(data.f_map[s], s));
+ data.p.insert_or_assign(s, n);
+ data.queue.insert(ext::make_tuple(std::max(data.f_map[s], 2 * data.g_map[s]), data.g_map[s], s));
+
+ f_update(s); // Update currently best path
+ }
+ }
+}
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+template<typename TNode, typename TWeight, typename F>
+void MM::init(MM::Data<TNode, TWeight> &data, const TNode &start, F f_heuristic) {
+ data.g_map[start] = 0;
+ data.g_set.insert(ext::make_pair(data.g_map[start], start));
+ data.f_map[start] = data.g_map[start] + f_heuristic(start);
+ data.f_set.insert(ext::make_pair(data.f_map[start], start));
+ data.p.insert_or_assign(start, start);
+ data.queue.insert(ext::make_tuple(std::max(data.f_map[start], 2 * data.g_map[start]),
+ data.g_map[start],
+ start));
+}
+
+// ---------------------------------------------------------------------------------------------------------------------
+
+} // namespace shortest_path
+#endif //ALIB2_MM_HPP
--
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