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yen_ksp.hpp
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yen_ksp.hpp
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// =======================================================================
// Copyright 2015 by Ireneusz Szcześniak
// Author: Ireneusz Szcześniak <www.irkos.org>
//
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
// =======================================================================
// =======================================================================
// This is the implementation of the Yen algorithm:
//
// Jin Y. Yen, Finding the k shortest loopless paths in a network,
// Management Science, vol. 17, no. 11, July 1971, pages 712-716
//
// Note 1: in the article there are Q^k Q_k Q^k_k used. As far as I
// can tell they have the same meaning. Q simply denotes the number
// of the node previous to the last node in a path (which always
// equals to the number of nodes in the path - 1), while (Q) denotes
// the node number Q in a path. For instance, in the path a-b-c-d,
// the number of the node previous to the last is Q = 3, while (Q) =
// c. Q^k refers to the k-th shortest path, and simply means the
// number of the node, which is previous to the last in the k-shortest
// path.
// =======================================================================
#ifndef BOOST_GRAPH_YEN_KSP
#define BOOST_GRAPH_YEN_KSP
#include <list>
#include <set>
#include <utility>
#include <boost/graph/dijkstra_shortest_paths.hpp>
#include <boost/graph/filtered_graph.hpp>
#include <boost/optional.hpp>
#include "custom_dijkstra_call.hpp"
namespace boost {
template <typename Graph, typename WeightMap, typename IndexMap>
std::list<std::pair<typename WeightMap::value_type,
std::list<typename Graph::edge_descriptor>>>
yen_ksp(const Graph& g,
typename Graph::vertex_descriptor s,
typename Graph::vertex_descriptor t,
WeightMap wm, IndexMap im, optional<unsigned> K)
{
typedef typename Graph::vertex_descriptor vertex_descriptor;
typedef typename Graph::edge_descriptor edge_descriptor;
typedef typename WeightMap::value_type weight_type;
typedef std::set<edge_descriptor> es_type;
typedef std::set<vertex_descriptor> vs_type;
typedef filtered_graph<Graph, is_not_in_subset<es_type>,
is_not_in_subset<vs_type>> fg_type;
typedef std::list<edge_descriptor> path_type;
typedef std::pair<weight_type, path_type> kr_type;
// The shortest paths - these we return.
std::list<kr_type> A;
// An empty result if the source and destination are the same.
if (s == t)
return A;
// The tentative paths - these are candidate paths. It's a set,
// because we want to make sure that a given result can show up in
// the set of tentative results only once. The problem is that
// the algorithm can find the same tentative path many times.
std::set<kr_type> B;
// Try to find the (optional) shortest path.
optional<kr_type> osp = custom_dijkstra_call(g, s, t, wm, im);
// We quit if there was no shortest path.
if (!osp)
return A;
// The first shortest path found becomes our first solution.
A.push_back(std::move(osp.get()));
// In each iteration we produce the next k-th shortest path.
for (int k = 2; !K || k <= K.get(); ++k)
{
// The previous shortest result and path.
const auto &psr = A.back();
const auto &psp = psr.second;
// The set of excluded edges. It's a set, because the
// algorithm can try to exclude an edge many times.
es_type exe;
// The set of excluded vertexes.
vs_type exv;
// The edge predicate.
is_not_in_subset<es_type> ep(exe);
// The vertex predicate.
is_not_in_subset<vs_type> vp(exv);
// The filtered graph.
fg_type fg(g, ep, vp);
// The root result: the cost and the root path.
kr_type rr;
// The root path.
const path_type &rp = rr.second;
// Use the previous shortest path to get tentative paths. We
// can go ahead with the loop without checking any condition
// (the condition in the for-statement is true): the path
// found must have at least one link, because s != t.
for(typename path_type::const_iterator i = psp.begin(); true;)
{
// An edge of the previous shortest path.
const edge_descriptor &edge = *i;
// The spur vertex - we try to deviate at this node.
const vertex_descriptor &sv = source(edge, g);
// Iterate over all previous shortest paths.
// An iteration examines j-th shortest path.
for(const auto &jr: A)
{
// The j-th shortest path.
const path_type &jp = jr.second;
// Let's prepare for the comparison.
typename path_type::const_iterator jpi = jp.begin();
typename path_type::const_iterator rpi = rp.begin();
// Iterate as long as the edges are equal.
while(jpi != jp.end() && rpi != rp.end() && *jpi == *rpi)
++jpi, ++rpi;
// Make sure we didn't reach the end of jp. If we
// did, there is no next edge in jp, which we could
// exclude. Also, make sure we reached the end of rp,
// i.e., the jp begins with the complete rp, and not a
// head of rp.
if (jpi != jp.end() && rpi == rp.end())
exe.insert(*jpi);
}
// Optional spur result.
optional<kr_type> osr = custom_dijkstra_call(fg, sv, t, wm, im);
if (osr)
{
// The tentative result.
kr_type tr = std::move(osr.get());
tr.first += rr.first;
tr.second.insert(tr.second.begin(), rp.begin(), rp.end());
B.insert(std::move(tr));
}
// We have the condition to break the look here, and not
// at the beginning, because we don't want to execute the
// remainer of the loop in vain.
if (++i == psp.end())
break;
// Remove the vertex that in this iteration is the spur,
// but in the next iteration it's going to be a vertex
// that should not be considered in the search for a spur
// path.
exv.insert(sv);
// Add the edge to the back of the root result.
rr.first += get(wm, edge);
rr.second.push_back(edge);
}
// Stop searching when there are no tentative paths.
if (B.empty())
break;
// Take the shortest tentative path and make it the next
// shortest path.
A.push_back(std::move(*B.begin()));
B.erase(B.begin());
}
return A;
}
template <typename Graph>
std::list<std::pair<typename property_map<Graph, edge_weight_t>::value_type,
std::list<typename Graph::edge_descriptor>>>
yen_ksp(Graph& g,
typename Graph::vertex_descriptor s,
typename Graph::vertex_descriptor t,
optional<unsigned> K = optional<unsigned>())
{
return yen_ksp(g, s, t, get(edge_weight_t(), g),
get(vertex_index_t(), g), K);
}
} // boost
#endif /* BOOST_GRAPH_YEN_KSP */