# HG changeset patch
# User Peter Kovacs <kpeter@inf.elte.hu>
# Date 1255647976 -7200
# Node ID ec0b1b423b8b100883ab1ef766204eb978363c80
# Parent 30c77d1c0cba549cb3f5309642d576cfa9c16534
Rework and improve Suurballe (#323)
- Improve the implementation: use a specific, faster variant of
residual Dijkstra for the first search.
- Some reorganizatiopn to make the code simpler.
- Small doc improvements.
diff -r 30c77d1c0cba -r ec0b1b423b8b lemon/suurballe.h
--- a/lemon/suurballe.h Thu Oct 15 21:04:50 2009 +0200
+++ b/lemon/suurballe.h Fri Oct 16 01:06:16 2009 +0200
@@ -46,7 +46,7 @@
/// 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.
@@ -57,7 +57,7 @@
///
/// \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>
@@ -109,39 +109,36 @@
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 +148,74 @@
// 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 +225,19 @@
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 +247,7 @@
// 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 +268,16 @@
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;
public:
@@ -258,7 +297,6 @@
~Suurballe() {
if (_local_flow) delete _flow;
if (_local_potential) delete _potential;
- delete _dijkstra;
}
/// \brief Set the flow map.
@@ -342,7 +380,7 @@
///
/// \param s The source node.
void init(const Node& s) {
- _source = s;
+ _s = s;
// Initialize maps
if (!_flow) {
@@ -372,20 +410,18 @@
///
/// \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);
// 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)) {
@@ -402,8 +438,8 @@
/// \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.
@@ -411,15 +447,15 @@
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;
}
}
@@ -518,7 +554,7 @@
/// \pre \ref run() or \ref findPaths() must be called before using
/// this function.
const Path& path(int i) const {
- return paths[i];
+ return _paths[i];
}
/// @}