diff options
Diffstat (limited to 'src/linkgraph')
-rw-r--r-- | src/linkgraph/linkgraphschedule.cpp | 3 | ||||
-rw-r--r-- | src/linkgraph/linkgraphschedule.h | 2 | ||||
-rw-r--r-- | src/linkgraph/mcf.cpp | 560 | ||||
-rw-r--r-- | src/linkgraph/mcf.h | 92 |
4 files changed, 656 insertions, 1 deletions
diff --git a/src/linkgraph/linkgraphschedule.cpp b/src/linkgraph/linkgraphschedule.cpp index b3e512506..2cb291853 100644 --- a/src/linkgraph/linkgraphschedule.cpp +++ b/src/linkgraph/linkgraphschedule.cpp @@ -13,6 +13,7 @@ #include "linkgraphschedule.h" #include "init.h" #include "demands.h" +#include "mcf.h" /** * Spawn a thread if possible and run the link graph job in the thread. If @@ -130,6 +131,8 @@ LinkGraphSchedule::LinkGraphSchedule() { this->handlers[0] = new InitHandler; this->handlers[1] = new DemandHandler; + this->handlers[2] = new MCFHandler<MCF1stPass>; + this->handlers[3] = new MCFHandler<MCF2ndPass>; } /** diff --git a/src/linkgraph/linkgraphschedule.h b/src/linkgraph/linkgraphschedule.h index 32e0dc6f4..f099f062b 100644 --- a/src/linkgraph/linkgraphschedule.h +++ b/src/linkgraph/linkgraphschedule.h @@ -44,7 +44,7 @@ private: friend const SaveLoad *GetLinkGraphScheduleDesc(); protected: - ComponentHandler *handlers[2]; ///< Handlers to be run for each job. + ComponentHandler *handlers[4]; ///< Handlers to be run for each job. GraphList schedule; ///< Queue for new jobs. JobList running; ///< Currently running jobs. diff --git a/src/linkgraph/mcf.cpp b/src/linkgraph/mcf.cpp new file mode 100644 index 000000000..d07f147b2 --- /dev/null +++ b/src/linkgraph/mcf.cpp @@ -0,0 +1,560 @@ +/** @file mcf.cpp Definition of Multi-Commodity-Flow solver. */ + +#include "../stdafx.h" +#include "../core/math_func.hpp" +#include "mcf.h" +#include <set> + +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]; + assert(edge.Distance() < UINT_MAX); + 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 = edge.Distance() + 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); + cycle_begin = path[cycle_begin->GetNode()]; + 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(); ++i) { + Path *new_child = *i; + 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; + } else { + Path *child = via_it->second; + uint new_flow = new_child->GetFlow(); + child->AddFlow(new_flow); + new_child->ReduceFlow(new_flow); + } + } + } + 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()); +} diff --git a/src/linkgraph/mcf.h b/src/linkgraph/mcf.h new file mode 100644 index 000000000..4ad598c57 --- /dev/null +++ b/src/linkgraph/mcf.h @@ -0,0 +1,92 @@ +/** @file mcf.h Declaration of Multi-Commodity-Flow solver */ + +#ifndef MCF_H +#define MCF_H + +#include "linkgraphjob_base.h" +#include <vector> + +typedef std::vector<Path *> PathVector; + +/** + * Multi-commodity flow calculating base class. + */ +class MultiCommodityFlow { +protected: + /** + * Constructor. + * @param job Link graph job being executed. + */ + MultiCommodityFlow(LinkGraphJob &job) : job(job), + max_saturation(job.Settings().short_path_saturation) + {} + + template<class Tannotation, class Tedge_iterator> + void Dijkstra(NodeID from, PathVector &paths); + + uint PushFlow(Edge &edge, Path *path, uint accuracy, uint max_saturation); + + void CleanupPaths(NodeID source, PathVector &paths); + + LinkGraphJob &job; ///< Job we're working with. + uint max_saturation; ///< Maximum saturation for edges. +}; + +/** + * First pass of the MCF calculation. Saturates shortest paths first, creates + * new paths if needed, eliminates cycles. This calculation is of exponential + * complexity in the number of nodes but the constant factors are sufficiently + * small to make it usable for most real-life link graph components. You can + * deal with performance problems that might occur here in multiple ways: + * - The overall accuracy is used here to determine how much flow is assigned + * in each loop. The lower the accuracy, the more flow is assigned, the less + * loops it takes to assign all flow. + * - The short_path_saturation setting determines when this pass stops. The + * lower you set it, the less flow will be assigned in this pass, the less + * time it will take. + * - You can increase the recalculation interval to allow for longer running + * times without creating lags. + */ +class MCF1stPass : public MultiCommodityFlow { +private: + bool EliminateCycles(); + bool EliminateCycles(PathVector &path, NodeID origin_id, NodeID next_id); + void EliminateCycle(PathVector &path, Path *cycle_begin, uint flow); + uint FindCycleFlow(const PathVector &path, const Path *cycle_begin); +public: + MCF1stPass(LinkGraphJob &job); +}; + +/** + * Second pass of the MCF calculation. Saturates paths with most capacity left + * first and doesn't create any paths along edges that haven't been visited in + * the first pass. This is why it doesn't have to do any cycle detection and + * elimination. As cycle detection is the most intense problem in the first + * pass this pass is cheaper. The accuracy is used here, too. + */ +class MCF2ndPass : public MultiCommodityFlow { +public: + MCF2ndPass(LinkGraphJob &job); +}; + +/** + * Link graph handler for MCF. Creates MultiCommodityFlow instance according to + * the template parameter. + */ +template<class Tpass> +class MCFHandler : public ComponentHandler { +public: + + /** + * Run the calculation. + * @param graph Component to be calculated. + */ + virtual void Run(LinkGraphJob &job) const { Tpass pass(job); } + + /** + * Destructor. Has to be given because of virtual Run(). + */ + virtual ~MCFHandler() {} +}; + +#endif /* MCF_H */ |