# HG changeset patch
# User Alpar Juttner <alpar@cs.elte.hu>
# Date 1267636457 0
# Node ID 5df6a8f29d5e48db8e1f4aa56cf10b3c99b1571d
# Parent e77b621e6e7ecd5a325e1546bdfd51aa01c7b395# Parent 9a7e4e606f83abbcec13b55a0a3a4e1a28b165aa
Merge #181, #323
diff -r e77b621e6e7e -r 5df6a8f29d5e lemon/suurballe.h
--- a/lemon/suurballe.h Mon Mar 01 07:51:45 2010 +0100
+++ b/lemon/suurballe.h Wed Mar 03 17:14:17 2010 +0000
@@ -29,6 +29,7 @@
#include <lemon/bin_heap.h>
#include <lemon/path.h>
#include <lemon/list_graph.h>
+#include <lemon/dijkstra.h>
#include <lemon/maps.h>
namespace lemon {
@@ -46,7 +47,7 @@
/// Note that this problem is a special case of the \ref min_cost_flow
/// "minimum cost flow problem". This implementation is actually an
/// efficient specialized version of the \ref CapacityScaling
- /// "Successive Shortest Path" algorithm directly for this problem.
+ /// "successive shortest path" algorithm directly for this problem.
/// Therefore this class provides query functions for flow values and
/// node potentials (the dual solution) just like the minimum cost flow
/// algorithms.
@@ -55,9 +56,9 @@
/// \tparam LEN The type of the length map.
/// The default value is <tt>GR::ArcMap<int></tt>.
///
- /// \warning Length values should be \e non-negative \e integers.
+ /// \warning Length values should be \e non-negative.
///
- /// \note For finding node-disjoint paths this algorithm can be used
+ /// \note For finding \e node-disjoint paths, this algorithm can be used
/// along with the \ref SplitNodes adaptor.
#ifdef DOXYGEN
template <typename GR, typename LEN>
@@ -97,6 +98,9 @@
private:
+ typedef typename Digraph::template NodeMap<int> HeapCrossRef;
+ typedef BinHeap<Length, HeapCrossRef> Heap;
+
// ResidualDijkstra is a special implementation of the
// Dijkstra algorithm for finding shortest paths in the
// residual network with respect to the reduced arc lengths
@@ -104,44 +108,38 @@
// distance of the nodes.
class ResidualDijkstra
{
- typedef typename Digraph::template NodeMap<int> HeapCrossRef;
- typedef BinHeap<Length, HeapCrossRef> Heap;
-
private:
- // The digraph the algorithm runs on
const Digraph &_graph;
-
- // The main maps
+ const LengthMap &_length;
const FlowMap &_flow;
- const LengthMap &_length;
- PotentialMap &_potential;
-
- // The distance map
- PotentialMap _dist;
- // The pred arc map
+ PotentialMap &_pi;
PredMap &_pred;
- // The processed (i.e. permanently labeled) nodes
- std::vector<Node> _proc_nodes;
-
Node _s;
Node _t;
+
+ PotentialMap _dist;
+ std::vector<Node> _proc_nodes;
public:
- /// Constructor.
- ResidualDijkstra( const Digraph &graph,
- const FlowMap &flow,
- const LengthMap &length,
- PotentialMap &potential,
- PredMap &pred,
- Node s, Node t ) :
- _graph(graph), _flow(flow), _length(length), _potential(potential),
- _dist(graph), _pred(pred), _s(s), _t(t) {}
+ // Constructor
+ ResidualDijkstra(Suurballe &srb) :
+ _graph(srb._graph), _length(srb._length),
+ _flow(*srb._flow), _pi(*srb._potential), _pred(srb._pred),
+ _s(srb._s), _t(srb._t), _dist(_graph) {}
+
+ // Run the algorithm and return true if a path is found
+ // from the source node to the target node.
+ bool run(int cnt) {
+ return cnt == 0 ? startFirst() : start();
+ }
- /// \brief Run the algorithm. It returns \c true if a path is found
- /// from the source node to the target node.
- bool run() {
+ private:
+
+ // Execute the algorithm for the first time (the flow and potential
+ // functions have to be identically zero).
+ bool startFirst() {
HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
Heap heap(heap_cross_ref);
heap.push(_s, 0);
@@ -151,29 +149,74 @@
// Process nodes
while (!heap.empty() && heap.top() != _t) {
Node u = heap.top(), v;
- Length d = heap.prio() + _potential[u], nd;
+ Length d = heap.prio(), dn;
_dist[u] = heap.prio();
+ _proc_nodes.push_back(u);
heap.pop();
+
+ // Traverse outgoing arcs
+ for (OutArcIt e(_graph, u); e != INVALID; ++e) {
+ v = _graph.target(e);
+ switch(heap.state(v)) {
+ case Heap::PRE_HEAP:
+ heap.push(v, d + _length[e]);
+ _pred[v] = e;
+ break;
+ case Heap::IN_HEAP:
+ dn = d + _length[e];
+ if (dn < heap[v]) {
+ heap.decrease(v, dn);
+ _pred[v] = e;
+ }
+ break;
+ case Heap::POST_HEAP:
+ break;
+ }
+ }
+ }
+ if (heap.empty()) return false;
+
+ // Update potentials of processed nodes
+ Length t_dist = heap.prio();
+ for (int i = 0; i < int(_proc_nodes.size()); ++i)
+ _pi[_proc_nodes[i]] = _dist[_proc_nodes[i]] - t_dist;
+ return true;
+ }
+
+ // Execute the algorithm.
+ bool start() {
+ HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
+ Heap heap(heap_cross_ref);
+ heap.push(_s, 0);
+ _pred[_s] = INVALID;
+ _proc_nodes.clear();
+
+ // Process nodes
+ while (!heap.empty() && heap.top() != _t) {
+ Node u = heap.top(), v;
+ Length d = heap.prio() + _pi[u], dn;
+ _dist[u] = heap.prio();
_proc_nodes.push_back(u);
+ heap.pop();
// Traverse outgoing arcs
for (OutArcIt e(_graph, u); e != INVALID; ++e) {
if (_flow[e] == 0) {
v = _graph.target(e);
switch(heap.state(v)) {
- case Heap::PRE_HEAP:
- heap.push(v, d + _length[e] - _potential[v]);
- _pred[v] = e;
- break;
- case Heap::IN_HEAP:
- nd = d + _length[e] - _potential[v];
- if (nd < heap[v]) {
- heap.decrease(v, nd);
+ case Heap::PRE_HEAP:
+ heap.push(v, d + _length[e] - _pi[v]);
_pred[v] = e;
- }
- break;
- case Heap::POST_HEAP:
- break;
+ break;
+ case Heap::IN_HEAP:
+ dn = d + _length[e] - _pi[v];
+ if (dn < heap[v]) {
+ heap.decrease(v, dn);
+ _pred[v] = e;
+ }
+ break;
+ case Heap::POST_HEAP:
+ break;
}
}
}
@@ -183,19 +226,19 @@
if (_flow[e] == 1) {
v = _graph.source(e);
switch(heap.state(v)) {
- case Heap::PRE_HEAP:
- heap.push(v, d - _length[e] - _potential[v]);
- _pred[v] = e;
- break;
- case Heap::IN_HEAP:
- nd = d - _length[e] - _potential[v];
- if (nd < heap[v]) {
- heap.decrease(v, nd);
+ case Heap::PRE_HEAP:
+ heap.push(v, d - _length[e] - _pi[v]);
_pred[v] = e;
- }
- break;
- case Heap::POST_HEAP:
- break;
+ break;
+ case Heap::IN_HEAP:
+ dn = d - _length[e] - _pi[v];
+ if (dn < heap[v]) {
+ heap.decrease(v, dn);
+ _pred[v] = e;
+ }
+ break;
+ case Heap::POST_HEAP:
+ break;
}
}
}
@@ -205,7 +248,7 @@
// Update potentials of processed nodes
Length t_dist = heap.prio();
for (int i = 0; i < int(_proc_nodes.size()); ++i)
- _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
+ _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
return true;
}
@@ -226,19 +269,21 @@
bool _local_potential;
// The source node
- Node _source;
+ Node _s;
// The target node
- Node _target;
+ Node _t;
// Container to store the found paths
- std::vector< SimplePath<Digraph> > paths;
+ std::vector<Path> _paths;
int _path_num;
// The pred arc map
PredMap _pred;
- // Implementation of the Dijkstra algorithm for finding augmenting
- // shortest paths in the residual network
- ResidualDijkstra *_dijkstra;
+
+ // Data for full init
+ PotentialMap *_init_dist;
+ PredMap *_init_pred;
+ bool _full_init;
public:
@@ -251,17 +296,16 @@
Suurballe( const Digraph &graph,
const LengthMap &length ) :
_graph(graph), _length(length), _flow(0), _local_flow(false),
- _potential(0), _local_potential(false), _pred(graph)
- {
- LEMON_ASSERT(std::numeric_limits<Length>::is_integer,
- "The length type of Suurballe must be integer");
- }
+ _potential(0), _local_potential(false), _pred(graph),
+ _init_dist(0), _init_pred(0)
+ {}
/// Destructor.
~Suurballe() {
if (_local_flow) delete _flow;
if (_local_potential) delete _potential;
- delete _dijkstra;
+ delete _init_dist;
+ delete _init_pred;
}
/// \brief Set the flow map.
@@ -306,10 +350,13 @@
/// \name Execution Control
/// The simplest way to execute the algorithm is to call the run()
- /// function.
- /// \n
+ /// function.\n
+ /// If you need to execute the algorithm many times using the same
+ /// source node, then you may call fullInit() once and start()
+ /// for each target node.\n
/// If you only need the flow that is the union of the found
- /// arc-disjoint paths, you may call init() and findFlow().
+ /// arc-disjoint paths, then you may call findFlow() instead of
+ /// start().
/// @{
@@ -329,23 +376,21 @@
/// just a shortcut of the following code.
/// \code
/// s.init(s);
- /// s.findFlow(t, k);
- /// s.findPaths();
+ /// s.start(t, k);
/// \endcode
int run(const Node& s, const Node& t, int k = 2) {
init(s);
- findFlow(t, k);
- findPaths();
+ start(t, k);
return _path_num;
}
/// \brief Initialize the algorithm.
///
- /// This function initializes the algorithm.
+ /// This function initializes the algorithm with the given source node.
///
/// \param s The source node.
void init(const Node& s) {
- _source = s;
+ _s = s;
// Initialize maps
if (!_flow) {
@@ -356,8 +401,63 @@
_potential = new PotentialMap(_graph);
_local_potential = true;
}
- for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0;
- for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0;
+ _full_init = false;
+ }
+
+ /// \brief Initialize the algorithm and perform Dijkstra.
+ ///
+ /// This function initializes the algorithm and performs a full
+ /// Dijkstra search from the given source node. It makes consecutive
+ /// executions of \ref start() "start(t, k)" faster, since they
+ /// have to perform %Dijkstra only k-1 times.
+ ///
+ /// This initialization is usually worth using instead of \ref init()
+ /// if the algorithm is executed many times using the same source node.
+ ///
+ /// \param s The source node.
+ void fullInit(const Node& s) {
+ // Initialize maps
+ init(s);
+ if (!_init_dist) {
+ _init_dist = new PotentialMap(_graph);
+ }
+ if (!_init_pred) {
+ _init_pred = new PredMap(_graph);
+ }
+
+ // Run a full Dijkstra
+ typename Dijkstra<Digraph, LengthMap>
+ ::template SetStandardHeap<Heap>
+ ::template SetDistMap<PotentialMap>
+ ::template SetPredMap<PredMap>
+ ::Create dijk(_graph, _length);
+ dijk.distMap(*_init_dist).predMap(*_init_pred);
+ dijk.run(s);
+
+ _full_init = true;
+ }
+
+ /// \brief Execute the algorithm.
+ ///
+ /// This function executes the algorithm.
+ ///
+ /// \param t The target node.
+ /// \param k The number of paths to be found.
+ ///
+ /// \return \c k if there are at least \c k arc-disjoint paths from
+ /// \c s to \c t in the digraph. Otherwise it returns the number of
+ /// arc-disjoint paths found.
+ ///
+ /// \note Apart from the return value, <tt>s.start(t, k)</tt> is
+ /// just a shortcut of the following code.
+ /// \code
+ /// s.findFlow(t, k);
+ /// s.findPaths();
+ /// \endcode
+ int start(const Node& t, int k = 2) {
+ findFlow(t, k);
+ findPaths();
+ return _path_num;
}
/// \brief Execute the algorithm to find an optimal flow.
@@ -375,20 +475,39 @@
///
/// \pre \ref init() must be called before using this function.
int findFlow(const Node& t, int k = 2) {
- _target = t;
- _dijkstra =
- new ResidualDijkstra( _graph, *_flow, _length, *_potential, _pred,
- _source, _target );
+ _t = t;
+ ResidualDijkstra dijkstra(*this);
+
+ // Initialization
+ for (ArcIt e(_graph); e != INVALID; ++e) {
+ (*_flow)[e] = 0;
+ }
+ if (_full_init) {
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ (*_potential)[n] = (*_init_dist)[n];
+ }
+ Node u = _t;
+ Arc e;
+ while ((e = (*_init_pred)[u]) != INVALID) {
+ (*_flow)[e] = 1;
+ u = _graph.source(e);
+ }
+ _path_num = 1;
+ } else {
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ (*_potential)[n] = 0;
+ }
+ _path_num = 0;
+ }
// Find shortest paths
- _path_num = 0;
while (_path_num < k) {
// Run Dijkstra
- if (!_dijkstra->run()) break;
+ if (!dijkstra.run(_path_num)) break;
++_path_num;
// Set the flow along the found shortest path
- Node u = _target;
+ Node u = _t;
Arc e;
while ((e = _pred[u]) != INVALID) {
if (u == _graph.target(e)) {
@@ -405,8 +524,8 @@
/// \brief Compute the paths from the flow.
///
- /// This function computes the paths from the found minimum cost flow,
- /// which is the union of some arc-disjoint paths.
+ /// This function computes arc-disjoint paths from the found minimum
+ /// cost flow, which is the union of them.
///
/// \pre \ref init() and \ref findFlow() must be called before using
/// this function.
@@ -414,15 +533,15 @@
FlowMap res_flow(_graph);
for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a];
- paths.clear();
- paths.resize(_path_num);
+ _paths.clear();
+ _paths.resize(_path_num);
for (int i = 0; i < _path_num; ++i) {
- Node n = _source;
- while (n != _target) {
+ Node n = _s;
+ while (n != _t) {
OutArcIt e(_graph, n);
for ( ; res_flow[e] == 0; ++e) ;
n = _graph.target(e);
- paths[i].addBack(e);
+ _paths[i].addBack(e);
res_flow[e] = 0;
}
}
@@ -520,8 +639,8 @@
///
/// \pre \ref run() or \ref findPaths() must be called before using
/// this function.
- Path path(int i) const {
- return paths[i];
+ const Path& path(int i) const {
+ return _paths[i];
}
/// @}
diff -r e77b621e6e7e -r 5df6a8f29d5e test/suurballe_test.cc
--- a/test/suurballe_test.cc Mon Mar 01 07:51:45 2010 +0100
+++ b/test/suurballe_test.cc Wed Mar 03 17:14:17 2010 +0000
@@ -101,6 +101,9 @@
k = suurb_test.run(n, n);
k = suurb_test.run(n, n, k);
suurb_test.init(n);
+ suurb_test.fullInit(n);
+ suurb_test.start(n);
+ suurb_test.start(n, k);
k = suurb_test.findFlow(n);
k = suurb_test.findFlow(n, k);
suurb_test.findPaths();