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catalan - 3 changes by juanjo
dutch - 4 changes by habell
russian - 4 changes by Lone_Wolf
spanish - 10 changes by juanjo
tamil - 7 changes by ganesh
catalan - 3 changes by juanjo
dutch - 4 changes by habell
russian - 4 changes by Lone_Wolf
spanish - 10 changes by juanjo
tamil - 7 changes by ganesh
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#include "../stdafx.h"
#include "../core/math_func.hpp"
#include "mcf.h"
#include <set>
#include "../safeguards.h"
typedef std::map<NodeID, Path *> PathViaMap;
/**
* Distance-based annotation for use in the Dijkstra algorithm. This is close
* to the original meaning of "annotation" in this context. Paths are rated
* according to the sum of distances of their edges.
*/
class DistanceAnnotation : public Path {
public:
/**
* Constructor.
* @param n ID of node to be annotated.
* @param source If the node is the source of its path.
*/
DistanceAnnotation(NodeID n, bool source = false) : Path(n, source) {}
bool IsBetter(const DistanceAnnotation *base, uint cap, int free_cap, uint dist) const;
/**
* Return the actual value of the annotation, in this case the distance.
* @return Distance.
*/
inline uint GetAnnotation() const { return this->distance; }
/**
* Comparator for std containers.
*/
struct Comparator {
bool operator()(const DistanceAnnotation *x, const DistanceAnnotation *y) const;
};
};
/**
* Capacity-based annotation for use in the Dijkstra algorithm. This annotation
* rates paths according to the maximum capacity of their edges. The Dijkstra
* algorithm still gives meaningful results like this as the capacity of a path
* can only decrease or stay the same if you add more edges.
*/
class CapacityAnnotation : public Path {
public:
/**
* Constructor.
* @param n ID of node to be annotated.
* @param source If the node is the source of its path.
*/
CapacityAnnotation(NodeID n, bool source = false) : Path(n, source) {}
bool IsBetter(const CapacityAnnotation *base, uint cap, int free_cap, uint dist) const;
/**
* Return the actual value of the annotation, in this case the capacity.
* @return Capacity.
*/
inline int GetAnnotation() const { return this->GetCapacityRatio(); }
/**
* Comparator for std containers.
*/
struct Comparator {
bool operator()(const CapacityAnnotation *x, const CapacityAnnotation *y) const;
};
};
/**
* Iterator class for getting the edges in the order of their next_edge
* members.
*/
class GraphEdgeIterator {
private:
LinkGraphJob &job; ///< Job being executed
EdgeIterator i; ///< Iterator pointing to current edge.
EdgeIterator end; ///< Iterator pointing beyond last edge.
public:
/**
* Construct a GraphEdgeIterator.
* @param job Job to iterate on.
*/
GraphEdgeIterator(LinkGraphJob &job) : job(job),
i(NULL, NULL, INVALID_NODE), end(NULL, NULL, INVALID_NODE)
{}
/**
* Setup the node to start iterating at.
* @param source Unused.
* @param node Node to start iterating at.
*/
void SetNode(NodeID source, NodeID node)
{
this->i = this->job[node].Begin();
this->end = this->job[node].End();
}
/**
* Retrieve the ID of the node the next edge points to.
* @return Next edge's target node ID or INVALID_NODE.
*/
NodeID Next()
{
return this->i != this->end ? (this->i++)->first : INVALID_NODE;
}
};
/**
* Iterator class for getting edges from a FlowStatMap.
*/
class FlowEdgeIterator {
private:
LinkGraphJob &job; ///< Link graph job we're working with.
/** Lookup table for getting NodeIDs from StationIDs. */
std::map<StationID, NodeID> station_to_node;
/** Current iterator in the shares map. */
FlowStat::SharesMap::const_iterator it;
/** End of the shares map. */
FlowStat::SharesMap::const_iterator end;
public:
/**
* Constructor.
* @param job Link graph job to work with.
*/
FlowEdgeIterator(LinkGraphJob &job) : job(job)
{
for (NodeID i = 0; i < job.Size(); ++i) {
this->station_to_node[job[i].Station()] = i;
}
}
/**
* Setup the node to retrieve edges from.
* @param source Root of the current path tree.
* @param node Current node to be checked for outgoing flows.
*/
void SetNode(NodeID source, NodeID node)
{
static const FlowStat::SharesMap empty;
const FlowStatMap &flows = this->job[node].Flows();
FlowStatMap::const_iterator it = flows.find(this->job[source].Station());
if (it != flows.end()) {
this->it = it->second.GetShares()->begin();
this->end = it->second.GetShares()->end();
} else {
this->it = empty.begin();
this->end = empty.end();
}
}
/**
* Get the next node for which a flow exists.
* @return ID of next node with flow.
*/
NodeID Next()
{
if (this->it == this->end) return INVALID_NODE;
return this->station_to_node[(this->it++)->second];
}
};
/**
* Determines if an extension to the given Path with the given parameters is
* better than this path.
* @param base Other path.
* @param cap Capacity of the new edge to be added to base.
* @param dist Distance of the new edge.
* @return True if base + the new edge would be better than the path associated
* with this annotation.
*/
bool DistanceAnnotation::IsBetter(const DistanceAnnotation *base, uint cap,
int free_cap, uint dist) const
{
/* If any of the paths is disconnected, the other one is better. If both
* are disconnected, this path is better.*/
if (base->distance == UINT_MAX) {
return false;
} else if (this->distance == UINT_MAX) {
return true;
}
if (free_cap > 0 && base->free_capacity > 0) {
/* If both paths have capacity left, compare their distances.
* If the other path has capacity left and this one hasn't, the
* other one's better (thus, return true). */
return this->free_capacity > 0 ? (base->distance + dist < this->distance) : true;
} else {
/* If the other path doesn't have capacity left, but this one has,
* the other one is worse (thus, return false).
* If both paths are out of capacity, do the regular distance
* comparison. */
return this->free_capacity > 0 ? false : (base->distance + dist < this->distance);
}
}
/**
* Determines if an extension to the given Path with the given parameters is
* better than this path.
* @param base Other path.
* @param cap Capacity of the new edge to be added to base.
* @param dist Distance of the new edge.
* @return True if base + the new edge would be better than the path associated
* with this annotation.
*/
bool CapacityAnnotation::IsBetter(const CapacityAnnotation *base, uint cap,
int free_cap, uint dist) const
{
int min_cap = Path::GetCapacityRatio(min(base->free_capacity, free_cap), min(base->capacity, cap));
int this_cap = this->GetCapacityRatio();
if (min_cap == this_cap) {
/* If the capacities are the same and the other path isn't disconnected
* choose the shorter path. */
return base->distance == UINT_MAX ? false : (base->distance + dist < this->distance);
} else {
return min_cap > this_cap;
}
}
/**
* A slightly modified Dijkstra algorithm. Grades the paths not necessarily by
* distance, but by the value Tannotation computes. It uses the max_saturation
* setting to artificially decrease capacities.
* @tparam Tannotation Annotation to be used.
* @tparam Tedge_iterator Iterator to be used for getting outgoing edges.
* @param source_node Node where the algorithm starts.
* @param paths Container for the paths to be calculated.
*/
template<class Tannotation, class Tedge_iterator>
void MultiCommodityFlow::Dijkstra(NodeID source_node, PathVector &paths)
{
typedef std::set<Tannotation *, typename Tannotation::Comparator> AnnoSet;
Tedge_iterator iter(this->job);
uint size = this->job.Size();
AnnoSet annos;
paths.resize(size, NULL);
for (NodeID node = 0; node < size; ++node) {
Tannotation *anno = new Tannotation(node, node == source_node);
annos.insert(anno);
paths[node] = anno;
}
while (!annos.empty()) {
typename AnnoSet::iterator i = annos.begin();
Tannotation *source = *i;
annos.erase(i);
NodeID from = source->GetNode();
iter.SetNode(source_node, from);
for (NodeID to = iter.Next(); to != INVALID_NODE; to = iter.Next()) {
if (to == from) continue; // Not a real edge but a consumption sign.
Edge edge = this->job[from][to];
uint capacity = edge.Capacity();
if (this->max_saturation != UINT_MAX) {
capacity *= this->max_saturation;
capacity /= 100;
if (capacity == 0) capacity = 1;
}
/* punish in-between stops a little */
uint distance = DistanceMaxPlusManhattan(this->job[from].XY(), this->job[to].XY()) + 1;
Tannotation *dest = static_cast<Tannotation *>(paths[to]);
if (dest->IsBetter(source, capacity, capacity - edge.Flow(), distance)) {
annos.erase(dest);
dest->Fork(source, capacity, capacity - edge.Flow(), distance);
annos.insert(dest);
}
}
}
}
/**
* Clean up paths that lead nowhere and the root path.
* @param source_id ID of the root node.
* @param paths Paths to be cleaned up.
*/
void MultiCommodityFlow::CleanupPaths(NodeID source_id, PathVector &paths)
{
Path *source = paths[source_id];
paths[source_id] = NULL;
for (PathVector::iterator i = paths.begin(); i != paths.end(); ++i) {
Path *path = *i;
if (path == NULL) continue;
if (path->GetParent() == source) path->Detach();
while (path != source && path != NULL && path->GetFlow() == 0) {
Path *parent = path->GetParent();
path->Detach();
if (path->GetNumChildren() == 0) {
paths[path->GetNode()] = NULL;
delete path;
}
path = parent;
}
}
delete source;
paths.clear();
}
/**
* Push flow along a path and update the unsatisfied_demand of the associated
* edge.
* @param edge Edge whose ends the path connects.
* @param path End of the path the flow should be pushed on.
* @param accuracy Accuracy of the calculation.
* @param max_saturation If < UINT_MAX only push flow up to the given
* saturation, otherwise the path can be "overloaded".
*/
uint MultiCommodityFlow::PushFlow(Edge &edge, Path *path, uint accuracy,
uint max_saturation)
{
assert(edge.UnsatisfiedDemand() > 0);
uint flow = Clamp(edge.Demand() / accuracy, 1, edge.UnsatisfiedDemand());
flow = path->AddFlow(flow, this->job, max_saturation);
edge.SatisfyDemand(flow);
return flow;
}
/**
* Find the flow along a cycle including cycle_begin in path.
* @param path Set of paths that form the cycle.
* @param cycle_begin Path to start at.
* @return Flow along the cycle.
*/
uint MCF1stPass::FindCycleFlow(const PathVector &path, const Path *cycle_begin)
{
uint flow = UINT_MAX;
const Path *cycle_end = cycle_begin;
do {
flow = min(flow, cycle_begin->GetFlow());
cycle_begin = path[cycle_begin->GetNode()];
} while (cycle_begin != cycle_end);
return flow;
}
/**
* Eliminate a cycle of the given flow in the given set of paths.
* @param path Set of paths containing the cycle.
* @param cycle_begin Part of the cycle to start at.
* @param flow Flow along the cycle.
*/
void MCF1stPass::EliminateCycle(PathVector &path, Path *cycle_begin, uint flow)
{
Path *cycle_end = cycle_begin;
do {
NodeID prev = cycle_begin->GetNode();
cycle_begin->ReduceFlow(flow);
if (cycle_begin->GetFlow() == 0) {
PathList &node_paths = this->job[cycle_begin->GetParent()->GetNode()].Paths();
for (PathList::iterator i = node_paths.begin(); i != node_paths.end(); ++i) {
if (*i == cycle_begin) {
node_paths.erase(i);
node_paths.push_back(cycle_begin);
break;
}
}
}
cycle_begin = path[prev];
Edge edge = this->job[prev][cycle_begin->GetNode()];
edge.RemoveFlow(flow);
} while (cycle_begin != cycle_end);
}
/**
* Eliminate cycles for origin_id in the graph. Start searching at next_id and
* work recursively. Also "summarize" paths: Add up the flows along parallel
* paths in one.
* @param path Paths checked in parent calls to this method.
* @param origin_id Origin of the paths to be checked.
* @param next_id Next node to be checked.
* @return If any cycles have been found and eliminated.
*/
bool MCF1stPass::EliminateCycles(PathVector &path, NodeID origin_id, NodeID next_id)
{
static Path *invalid_path = new Path(INVALID_NODE, true);
Path *at_next_pos = path[next_id];
/* this node has already been searched */
if (at_next_pos == invalid_path) return false;
if (at_next_pos == NULL) {
/* Summarize paths; add up the paths with the same source and next hop
* in one path each. */
PathList &paths = this->job[next_id].Paths();
PathViaMap next_hops;
for (PathList::iterator i = paths.begin(); i != paths.end();) {
Path *new_child = *i;
uint new_flow = new_child->GetFlow();
if (new_flow == 0) break;
if (new_child->GetOrigin() == origin_id) {
PathViaMap::iterator via_it = next_hops.find(new_child->GetNode());
if (via_it == next_hops.end()) {
next_hops[new_child->GetNode()] = new_child;
++i;
} else {
Path *child = via_it->second;
child->AddFlow(new_flow);
new_child->ReduceFlow(new_flow);
/* We might hit end() with with the ++ here and skip the
* newly push_back'ed path. That's good as the flow of that
* path is 0 anyway. */
paths.erase(i++);
paths.push_back(new_child);
}
} else {
++i;
}
}
bool found = false;
/* Search the next hops for nodes we have already visited */
for (PathViaMap::iterator via_it = next_hops.begin();
via_it != next_hops.end(); ++via_it) {
Path *child = via_it->second;
if (child->GetFlow() > 0) {
/* Push one child into the path vector and search this child's
* children. */
path[next_id] = child;
found = this->EliminateCycles(path, origin_id, child->GetNode()) || found;
}
}
/* All paths departing from this node have been searched. Mark as
* resolved if no cycles found. If cycles were found further cycles
* could be found in this branch, thus it has to be searched again next
* time we spot it.
*/
path[next_id] = found ? NULL : invalid_path;
return found;
}
/* This node has already been visited => we have a cycle.
* Backtrack to find the exact flow. */
uint flow = this->FindCycleFlow(path, at_next_pos);
if (flow > 0) {
this->EliminateCycle(path, at_next_pos, flow);
return true;
}
return false;
}
/**
* Eliminate all cycles in the graph. Check paths starting at each node for
* potential cycles.
* @return If any cycles have been found and eliminated.
*/
bool MCF1stPass::EliminateCycles()
{
bool cycles_found = false;
uint size = this->job.Size();
PathVector path(size, NULL);
for (NodeID node = 0; node < size; ++node) {
/* Starting at each node in the graph find all cycles involving this
* node. */
std::fill(path.begin(), path.end(), (Path *)NULL);
cycles_found |= this->EliminateCycles(path, node, node);
}
return cycles_found;
}
/**
* Run the first pass of the MCF calculation.
* @param job Link graph job to calculate.
*/
MCF1stPass::MCF1stPass(LinkGraphJob &job) : MultiCommodityFlow(job)
{
PathVector paths;
uint size = job.Size();
uint accuracy = job.Settings().accuracy;
bool more_loops;
do {
more_loops = false;
for (NodeID source = 0; source < size; ++source) {
/* First saturate the shortest paths. */
this->Dijkstra<DistanceAnnotation, GraphEdgeIterator>(source, paths);
for (NodeID dest = 0; dest < size; ++dest) {
Edge edge = job[source][dest];
if (edge.UnsatisfiedDemand() > 0) {
Path *path = paths[dest];
assert(path != NULL);
/* Generally only allow paths that don't exceed the
* available capacity. But if no demand has been assigned
* yet, make an exception and allow any valid path *once*. */
if (path->GetFreeCapacity() > 0 && this->PushFlow(edge, path,
accuracy, this->max_saturation) > 0) {
/* If a path has been found there is a chance we can
* find more. */
more_loops = more_loops || (edge.UnsatisfiedDemand() > 0);
} else if (edge.UnsatisfiedDemand() == edge.Demand() &&
path->GetFreeCapacity() > INT_MIN) {
this->PushFlow(edge, path, accuracy, UINT_MAX);
}
}
}
this->CleanupPaths(source, paths);
}
} while (more_loops || this->EliminateCycles());
}
/**
* Run the second pass of the MCF calculation which assigns all remaining
* demands to existing paths.
* @param job Link graph job to calculate.
*/
MCF2ndPass::MCF2ndPass(LinkGraphJob &job) : MultiCommodityFlow(job)
{
this->max_saturation = UINT_MAX; // disable artificial cap on saturation
PathVector paths;
uint size = job.Size();
uint accuracy = job.Settings().accuracy;
bool demand_left = true;
while (demand_left) {
demand_left = false;
for (NodeID source = 0; source < size; ++source) {
this->Dijkstra<CapacityAnnotation, FlowEdgeIterator>(source, paths);
for (NodeID dest = 0; dest < size; ++dest) {
Edge edge = this->job[source][dest];
Path *path = paths[dest];
if (edge.UnsatisfiedDemand() > 0 && path->GetFreeCapacity() > INT_MIN) {
this->PushFlow(edge, path, accuracy, UINT_MAX);
if (edge.UnsatisfiedDemand() > 0) demand_left = true;
}
}
this->CleanupPaths(source, paths);
}
}
}
/**
* Relation that creates a weak order without duplicates.
* Avoid accidentally deleting different paths of the same capacity/distance in
* a set. When the annotation is the same node IDs are compared, so there are
* no equal ranges.
* @tparam T Type to be compared on.
* @param x_anno First value.
* @param y_anno Second value.
* @param x Node id associated with the first value.
* @param y Node id associated with the second value.
*/
template <typename T>
bool Greater(T x_anno, T y_anno, NodeID x, NodeID y)
{
if (x_anno > y_anno) return true;
if (x_anno < y_anno) return false;
return x > y;
}
/**
* Compare two capacity annotations.
* @param x First capacity annotation.
* @param y Second capacity annotation.
* @return If x is better than y.
*/
bool CapacityAnnotation::Comparator::operator()(const CapacityAnnotation *x,
const CapacityAnnotation *y) const
{
return x != y && Greater<int>(x->GetAnnotation(), y->GetAnnotation(),
x->GetNode(), y->GetNode());
}
/**
* Compare two distance annotations.
* @param x First distance annotation.
* @param y Second distance annotation.
* @return If x is better than y.
*/
bool DistanceAnnotation::Comparator::operator()(const DistanceAnnotation *x,
const DistanceAnnotation *y) const
{
return x != y && !Greater<uint>(x->GetAnnotation(), y->GetAnnotation(),
x->GetNode(), y->GetNode());
}
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