mcf.cpp

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00001 
00003 #include "../stdafx.h"
00004 #include "../core/math_func.hpp"
00005 #include "mcf.h"
00006 
00007 typedef std::map<NodeID, Path *> PathViaMap;
00008 
00014 class DistanceAnnotation : public Path {
00015 public:
00016 
00022   DistanceAnnotation(NodeID n, bool source = false) : Path(n, source) {}
00023 
00024   bool IsBetter(const DistanceAnnotation *base, uint cap, int free_cap, uint dist) const;
00025 
00030   inline uint GetAnnotation() const { return this->distance; }
00031 
00035   struct Comparator {
00036     bool operator()(const DistanceAnnotation *x, const DistanceAnnotation *y) const;
00037   };
00038 };
00039 
00046 class CapacityAnnotation : public Path {
00047 public:
00048 
00054   CapacityAnnotation(NodeID n, bool source = false) : Path(n, source) {}
00055 
00056   bool IsBetter(const CapacityAnnotation *base, uint cap, int free_cap, uint dist) const;
00057 
00062   inline int GetAnnotation() const { return this->GetCapacityRatio(); }
00063 
00067   struct Comparator {
00068     bool operator()(const CapacityAnnotation *x, const CapacityAnnotation *y) const;
00069   };
00070 };
00071 
00076 class GraphEdgeIterator {
00077 private:
00078   LinkGraphJob &job; 
00079   EdgeIterator i;    
00080   EdgeIterator end;  
00081 
00082 public:
00083 
00088   GraphEdgeIterator(LinkGraphJob &job) : job(job),
00089     i(NULL, NULL, INVALID_NODE), end(NULL, NULL, INVALID_NODE)
00090   {}
00091 
00097   void SetNode(NodeID source, NodeID node)
00098   {
00099     this->i = this->job[node].Begin();
00100     this->end = this->job[node].End();
00101   }
00102 
00107   NodeID Next()
00108   {
00109     return this->i != this->end ? (this->i++)->first : INVALID_NODE;
00110   }
00111 };
00112 
00116 class FlowEdgeIterator {
00117 private:
00118   LinkGraphJob &job; 
00119 
00121   std::map<StationID, NodeID> station_to_node;
00122 
00124   FlowStat::SharesMap::const_iterator it;
00125 
00127   FlowStat::SharesMap::const_iterator end;
00128 public:
00129 
00134   FlowEdgeIterator(LinkGraphJob &job) : job(job)
00135   {
00136     for (NodeID i = 0; i < job.Size(); ++i) {
00137       this->station_to_node[job[i].Station()] = i;
00138     }
00139   }
00140 
00146   void SetNode(NodeID source, NodeID node)
00147   {
00148     static const FlowStat::SharesMap empty;
00149     const FlowStatMap &flows = this->job[node].Flows();
00150     FlowStatMap::const_iterator it = flows.find(this->job[source].Station());
00151     if (it != flows.end()) {
00152       this->it = it->second.GetShares()->begin();
00153       this->end = it->second.GetShares()->end();
00154     } else {
00155       this->it = empty.begin();
00156       this->end = empty.end();
00157     }
00158   }
00159 
00164   NodeID Next()
00165   {
00166     if (this->it == this->end) return INVALID_NODE;
00167     return this->station_to_node[(this->it++)->second];
00168   }
00169 };
00170 
00180 bool DistanceAnnotation::IsBetter(const DistanceAnnotation *base, uint cap,
00181     int free_cap, uint dist) const
00182 {
00183   /* If any of the paths is disconnected, the other one is better. If both
00184    * are disconnected, this path is better.*/
00185   if (base->distance == UINT_MAX) {
00186     return false;
00187   } else if (this->distance == UINT_MAX) {
00188     return true;
00189   }
00190 
00191   if (free_cap > 0 && base->free_capacity > 0) {
00192     /* If both paths have capacity left, compare their distances.
00193      * If the other path has capacity left and this one hasn't, the
00194      * other one's better (thus, return true). */
00195     return this->free_capacity > 0 ? (base->distance + dist < this->distance) : true;
00196   } else {
00197     /* If the other path doesn't have capacity left, but this one has,
00198      * the other one is worse (thus, return false).
00199      * If both paths are out of capacity, do the regular distance
00200      * comparison. */
00201     return this->free_capacity > 0 ? false : (base->distance + dist < this->distance);
00202   }
00203 }
00204 
00214 bool CapacityAnnotation::IsBetter(const CapacityAnnotation *base, uint cap,
00215     int free_cap, uint dist) const
00216 {
00217   int min_cap = Path::GetCapacityRatio(min(base->free_capacity, free_cap), min(base->capacity, cap));
00218   int this_cap = this->GetCapacityRatio();
00219   if (min_cap == this_cap) {
00220     /* If the capacities are the same and the other path isn't disconnected
00221      * choose the shorter path. */
00222     return base->distance == UINT_MAX ? false : (base->distance + dist < this->distance);
00223   } else {
00224     return min_cap > this_cap;
00225   }
00226 }
00227 
00237 template<class Tannotation, class Tedge_iterator>
00238 void MultiCommodityFlow::Dijkstra(NodeID source_node, PathVector &paths)
00239 {
00240   typedef std::set<Tannotation *, typename Tannotation::Comparator> AnnoSet;
00241   Tedge_iterator iter(this->job);
00242   uint size = this->job.Size();
00243   AnnoSet annos;
00244   paths.resize(size, NULL);
00245   for (NodeID node = 0; node < size; ++node) {
00246     Tannotation *anno = new Tannotation(node, node == source_node);
00247     annos.insert(anno);
00248     paths[node] = anno;
00249   }
00250   while (!annos.empty()) {
00251     typename AnnoSet::iterator i = annos.begin();
00252     Tannotation *source = *i;
00253     annos.erase(i);
00254     NodeID from = source->GetNode();
00255     iter.SetNode(source_node, from);
00256     for (NodeID to = iter.Next(); to != INVALID_NODE; to = iter.Next()) {
00257       if (to == from) continue; // Not a real edge but a consumption sign.
00258       Edge edge = this->job[from][to];
00259       assert(edge.Distance() < UINT_MAX);
00260       uint capacity = edge.Capacity();
00261       if (this->max_saturation != UINT_MAX) {
00262         capacity *= this->max_saturation;
00263         capacity /= 100;
00264         if (capacity == 0) capacity = 1;
00265       }
00266       /* punish in-between stops a little */
00267       uint distance = edge.Distance() + 1;
00268       Tannotation *dest = static_cast<Tannotation *>(paths[to]);
00269       if (dest->IsBetter(source, capacity, capacity - edge.Flow(), distance)) {
00270         annos.erase(dest);
00271         dest->Fork(source, capacity, capacity - edge.Flow(), distance);
00272         annos.insert(dest);
00273       }
00274     }
00275   }
00276 }
00277 
00283 void MultiCommodityFlow::CleanupPaths(NodeID source_id, PathVector &paths)
00284 {
00285   Path *source = paths[source_id];
00286   paths[source_id] = NULL;
00287   for (PathVector::iterator i = paths.begin(); i != paths.end(); ++i) {
00288     Path *path = *i;
00289     if (path == NULL) continue;
00290     if (path->GetParent() == source) path->Detach();
00291     while (path != source && path != NULL && path->GetFlow() == 0) {
00292       Path *parent = path->GetParent();
00293       path->Detach();
00294       if (path->GetNumChildren() == 0) {
00295         paths[path->GetNode()] = NULL;
00296         delete path;
00297       }
00298       path = parent;
00299     }
00300   }
00301   delete source;
00302   paths.clear();
00303 }
00304 
00314 uint MultiCommodityFlow::PushFlow(Edge &edge, Path *path, uint accuracy,
00315     uint max_saturation)
00316 {
00317   assert(edge.UnsatisfiedDemand() > 0);
00318   uint flow = Clamp(edge.Demand() / accuracy, 1, edge.UnsatisfiedDemand());
00319   flow = path->AddFlow(flow, this->job, max_saturation);
00320   edge.SatisfyDemand(flow);
00321   return flow;
00322 }
00323 
00330 uint MCF1stPass::FindCycleFlow(const PathVector &path, const Path *cycle_begin)
00331 {
00332   uint flow = UINT_MAX;
00333   const Path *cycle_end = cycle_begin;
00334   do {
00335     flow = min(flow, cycle_begin->GetFlow());
00336     cycle_begin = path[cycle_begin->GetNode()];
00337   } while (cycle_begin != cycle_end);
00338   return flow;
00339 }
00340 
00347 void MCF1stPass::EliminateCycle(PathVector &path, Path *cycle_begin, uint flow)
00348 {
00349   Path *cycle_end = cycle_begin;
00350   do {
00351     NodeID prev = cycle_begin->GetNode();
00352     cycle_begin->ReduceFlow(flow);
00353     cycle_begin = path[cycle_begin->GetNode()];
00354     Edge edge = this->job[prev][cycle_begin->GetNode()];
00355     edge.RemoveFlow(flow);
00356   } while (cycle_begin != cycle_end);
00357 }
00358 
00368 bool MCF1stPass::EliminateCycles(PathVector &path, NodeID origin_id, NodeID next_id)
00369 {
00370   static Path *invalid_path = new Path(INVALID_NODE, true);
00371   Path *at_next_pos = path[next_id];
00372 
00373   /* this node has already been searched */
00374   if (at_next_pos == invalid_path) return false;
00375 
00376   if (at_next_pos == NULL) {
00377     /* Summarize paths; add up the paths with the same source and next hop
00378      * in one path each. */
00379     PathSet &paths = this->job[next_id].Paths();
00380     PathViaMap next_hops;
00381     for (PathSet::iterator i = paths.begin(); i != paths.end(); ++i) {
00382       Path *new_child = *i;
00383       if (new_child->GetOrigin() == origin_id) {
00384         PathViaMap::iterator via_it = next_hops.find(new_child->GetNode());
00385         if (via_it == next_hops.end()) {
00386           next_hops[new_child->GetNode()] = new_child;
00387         } else {
00388           Path *child = via_it->second;
00389           uint new_flow = new_child->GetFlow();
00390           child->AddFlow(new_flow);
00391           new_child->ReduceFlow(new_flow);
00392         }
00393       }
00394     }
00395     bool found = false;
00396     /* Search the next hops for nodes we have already visited */
00397     for (PathViaMap::iterator via_it = next_hops.begin();
00398         via_it != next_hops.end(); ++via_it) {
00399       Path *child = via_it->second;
00400       if (child->GetFlow() > 0) {
00401         /* Push one child into the path vector and search this child's
00402          * children. */
00403         path[next_id] = child;
00404         found = this->EliminateCycles(path, origin_id, child->GetNode()) || found;
00405       }
00406     }
00407     /* All paths departing from this node have been searched. Mark as
00408      * resolved if no cycles found. If cycles were found further cycles
00409      * could be found in this branch, thus it has to be searched again next
00410      * time we spot it.
00411      */
00412     path[next_id] = found ? NULL : invalid_path;
00413     return found;
00414   }
00415 
00416   /* This node has already been visited => we have a cycle.
00417    * Backtrack to find the exact flow. */
00418   uint flow = this->FindCycleFlow(path, at_next_pos);
00419   if (flow > 0) {
00420     this->EliminateCycle(path, at_next_pos, flow);
00421     return true;
00422   }
00423 
00424   return false;
00425 }
00426 
00432 bool MCF1stPass::EliminateCycles()
00433 {
00434   bool cycles_found = false;
00435   uint size = this->job.Size();
00436   PathVector path(size, NULL);
00437   for (NodeID node = 0; node < size; ++node) {
00438     /* Starting at each node in the graph find all cycles involving this
00439      * node. */
00440     std::fill(path.begin(), path.end(), (Path *)NULL);
00441     cycles_found |= this->EliminateCycles(path, node, node);
00442   }
00443   return cycles_found;
00444 }
00445 
00450 MCF1stPass::MCF1stPass(LinkGraphJob &job) : MultiCommodityFlow(job)
00451 {
00452   PathVector paths;
00453   uint size = job.Size();
00454   uint accuracy = job.Settings().accuracy;
00455   bool more_loops;
00456 
00457   do {
00458     more_loops = false;
00459     for (NodeID source = 0; source < size; ++source) {
00460       /* First saturate the shortest paths. */
00461       this->Dijkstra<DistanceAnnotation, GraphEdgeIterator>(source, paths);
00462 
00463       for (NodeID dest = 0; dest < size; ++dest) {
00464         Edge edge = job[source][dest];
00465         if (edge.UnsatisfiedDemand() > 0) {
00466           Path *path = paths[dest];
00467           assert(path != NULL);
00468           /* Generally only allow paths that don't exceed the
00469            * available capacity. But if no demand has been assigned
00470            * yet, make an exception and allow any valid path *once*. */
00471           if (path->GetFreeCapacity() > 0 && this->PushFlow(edge, path,
00472               accuracy, this->max_saturation) > 0) {
00473             /* If a path has been found there is a chance we can
00474              * find more. */
00475             more_loops = more_loops || (edge.UnsatisfiedDemand() > 0);
00476           } else if (edge.UnsatisfiedDemand() == edge.Demand() &&
00477               path->GetFreeCapacity() > INT_MIN) {
00478             this->PushFlow(edge, path, accuracy, UINT_MAX);
00479           }
00480         }
00481       }
00482       this->CleanupPaths(source, paths);
00483     }
00484   } while (more_loops || this->EliminateCycles());
00485 }
00486 
00492 MCF2ndPass::MCF2ndPass(LinkGraphJob &job) : MultiCommodityFlow(job)
00493 {
00494   this->max_saturation = UINT_MAX; // disable artificial cap on saturation
00495   PathVector paths;
00496   uint size = job.Size();
00497   uint accuracy = job.Settings().accuracy;
00498   bool demand_left = true;
00499   while (demand_left) {
00500     demand_left = false;
00501     for (NodeID source = 0; source < size; ++source) {
00502       this->Dijkstra<CapacityAnnotation, FlowEdgeIterator>(source, paths);
00503       for (NodeID dest = 0; dest < size; ++dest) {
00504         Edge edge = this->job[source][dest];
00505         Path *path = paths[dest];
00506         if (edge.UnsatisfiedDemand() > 0 && path->GetFreeCapacity() > INT_MIN) {
00507           this->PushFlow(edge, path, accuracy, UINT_MAX);
00508           if (edge.UnsatisfiedDemand() > 0) demand_left = true;
00509         }
00510       }
00511       this->CleanupPaths(source, paths);
00512     }
00513   }
00514 }
00515 
00527 template <typename T>
00528 bool Greater(T x_anno, T y_anno, NodeID x, NodeID y)
00529 {
00530   if (x_anno > y_anno) return true;
00531   if (x_anno < y_anno) return false;
00532   return x > y;
00533 }
00534 
00541 bool CapacityAnnotation::Comparator::operator()(const CapacityAnnotation *x,
00542     const CapacityAnnotation *y) const
00543 {
00544   return x != y && Greater<int>(x->GetAnnotation(), y->GetAnnotation(),
00545       x->GetNode(), y->GetNode());
00546 }
00547 
00554 bool DistanceAnnotation::Comparator::operator()(const DistanceAnnotation *x,
00555     const DistanceAnnotation *y) const
00556 {
00557   return x != y && !Greater<uint>(x->GetAnnotation(), y->GetAnnotation(),
00558       x->GetNode(), y->GetNode());
00559 }