mcf.cpp

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00001 
00003 #include "../stdafx.h"
00004 #include "../core/math_func.hpp"
00005 #include "mcf.h"
00006 
00016 bool DistanceAnnotation::IsBetter(const DistanceAnnotation *base, uint cap,
00017     int free_cap, uint dist) const
00018 {
00019   /* If any of the paths is disconnected, the other one is better. If both
00020    * are disconnected, this path is better.
00021    */
00022   if (base->distance == UINT_MAX) {
00023     return false;
00024   } else if (this->distance == UINT_MAX) {
00025     return true;
00026   }
00027 
00028   if (free_cap > 0 && base->free_capacity > 0) {
00029     /* If both paths have capacity left, compare their distances.
00030      * If the other path has capacity left and this one hasn't, the
00031      * other one's better.
00032      */
00033     return this->free_capacity > 0 ? (base->distance + dist < this->distance) : true;
00034   } else {
00035     /* If the other path doesn't have capacity left, but this one has,
00036      * this one is better.
00037      * If both paths are out of capacity, do the regular distance
00038      * comparison.
00039      */
00040     return this->free_capacity > 0 ? false : (base->distance + dist < this->distance);
00041   }
00042 }
00043 
00053 bool CapacityAnnotation::IsBetter(const CapacityAnnotation *base, uint cap,
00054     int free_cap, uint dist) const
00055 {
00056   int min_cap = (min(base->free_capacity, free_cap) << 4) / (min(base->capacity, cap) + 1);
00057   int this_cap = this->GetCapacityRatio();
00058   if (min_cap == this_cap) {
00059     /* If the capacities are the same and the other path isn't disconnected
00060      * choose the shorter path.
00061      */
00062     return base->distance == UINT_MAX ? false : (base->distance + dist < this->distance);
00063   } else {
00064     return min_cap > this_cap;
00065   }
00066 }
00067 
00081 template<class Tannotation>
00082 void MultiCommodityFlow::Dijkstra(NodeID source_node, PathVector &paths,
00083     bool create_new_paths)
00084 {
00085   typedef std::set<Tannotation *, typename Tannotation::Comparator> AnnoSet;
00086   uint size = this->graph->GetSize();
00087   StationID source_station = this->graph->GetNode(source_node).station;
00088   AnnoSet annos;
00089   paths.resize(size, NULL);
00090   for (NodeID node = 0; node < size; ++node) {
00091     Tannotation *anno = new Tannotation(node, node == source_node);
00092     annos.insert(anno);
00093     paths[node] = anno;
00094   }
00095   while (!annos.empty()) {
00096     typename AnnoSet::iterator i = annos.begin();
00097     Tannotation *source = *i;
00098     annos.erase(i);
00099     NodeID from = source->GetNode();
00100     NodeID to = this->graph->GetFirstEdge(from);
00101     while (to != INVALID_NODE) {
00102       Edge &edge = this->graph->GetEdge(from, to);
00103       assert(edge.distance < UINT_MAX);
00104       if (create_new_paths || this->graph->GetNode(from)
00105           .flows[source_station][this->graph->GetNode(to).station] > 0) {
00106         uint capacity = edge.capacity;
00107         if (create_new_paths) {
00108           capacity *= this->graph->GetSettings().short_path_saturation;
00109           capacity /= 100;
00110           if (capacity == 0) capacity = 1;
00111         }
00112         /* punish in-between stops a little */
00113         uint distance = edge.distance + 1;
00114         Tannotation *dest = static_cast<Tannotation *>(paths[to]);
00115         if (dest->IsBetter(source, capacity, capacity - edge.flow, distance)) {
00116           annos.erase(dest);
00117           dest->Fork(source, capacity, capacity - edge.flow, distance);
00118           annos.insert(dest);
00119         }
00120       }
00121       to = edge.next_edge;
00122     }
00123   }
00124 }
00125 
00131 void MultiCommodityFlow::CleanupPaths(NodeID source_id, PathVector &paths)
00132 {
00133   Path *source = paths[source_id];
00134   paths[source_id] = NULL;
00135   for (PathVector::iterator i = paths.begin(); i != paths.end(); ++i) {
00136     Path *path = *i;
00137     if (path == NULL) continue;
00138     if (path->GetParent() == source) path->Detach();
00139     while (path != source && path != NULL && path->GetFlow() == 0) {
00140       Path *parent = path->GetParent();
00141       path->Detach();
00142       if (path->GetNumChildren() == 0) {
00143         paths[path->GetNode()] = NULL;
00144         delete path;
00145       }
00146       path = parent;
00147     }
00148   }
00149   delete source;
00150   paths.clear();
00151 }
00152 
00162 uint MultiCommodityFlow::PushFlow(Edge &edge, Path *path, uint accuracy,
00163     bool positive_cap)
00164 {
00165   assert(edge.unsatisfied_demand > 0);
00166   uint flow = Clamp(edge.demand / accuracy, 1, edge.unsatisfied_demand);
00167   flow = path->AddFlow(flow, this->graph, positive_cap);
00168   edge.unsatisfied_demand -= flow;
00169   return flow;
00170 }
00171 
00178 uint MCF1stPass::FindCycleFlow(const PathVector &path, const Path *cycle_begin)
00179 {
00180   uint flow = UINT_MAX;
00181   const Path *cycle_end = cycle_begin;
00182   do {
00183     flow = min(flow, cycle_begin->GetFlow());
00184     cycle_begin = path[cycle_begin->GetNode()];
00185   } while (cycle_begin != cycle_end);
00186   return flow;
00187 }
00188 
00195 void MCF1stPass::EliminateCycle(PathVector &path, Path *cycle_begin, uint flow)
00196 {
00197   Path *cycle_end = cycle_begin;
00198   do {
00199     NodeID prev = cycle_begin->GetNode();
00200     cycle_begin->ReduceFlow(flow);
00201     cycle_begin = path[cycle_begin->GetNode()];
00202     Edge &edge = this->graph->GetEdge(prev, cycle_begin->GetNode());
00203     edge.flow -= flow;
00204   } while (cycle_begin != cycle_end);
00205 }
00206 
00216 bool MCF1stPass::EliminateCycles(PathVector &path, NodeID origin_id, NodeID next_id)
00217 {
00218   static Path *invalid_path = new Path(INVALID_NODE, true);
00219   Path *at_next_pos = path[next_id];
00220   if (at_next_pos == invalid_path) {
00221     /* this node has already been searched */
00222     return false;
00223   } else if (at_next_pos == NULL) {
00224     /* summarize paths; add up the paths with the same source and next hop
00225      * in one path each
00226      */
00227     PathSet &paths = this->graph->GetNode(next_id).paths;
00228     PathViaMap next_hops;
00229     for (PathSet::iterator i = paths.begin(); i != paths.end(); ++i) {
00230       Path *new_child = *i;
00231       if (new_child->GetOrigin() == origin_id) {
00232         PathViaMap::iterator via_it = next_hops.find(new_child->GetNode());
00233         if (via_it == next_hops.end()) {
00234           next_hops[new_child->GetNode()] = new_child;
00235         } else {
00236           Path *child = via_it->second;
00237           uint new_flow = new_child->GetFlow();
00238           child->AddFlow(new_flow);
00239           new_child->ReduceFlow(new_flow);
00240         }
00241       }
00242     }
00243     bool found = false;
00244     /* search the next hops for nodes we have already visited */
00245     for (PathViaMap::iterator via_it = next_hops.begin();
00246         via_it != next_hops.end(); ++via_it) {
00247       Path *child = via_it->second;
00248       if (child->GetFlow() > 0) {
00249         /* push one child into the path vector and search this child's
00250          * children
00251          */
00252         path[next_id] = child;
00253         found = this->EliminateCycles(path, origin_id, child->GetNode()) || found;
00254       }
00255     }
00256     /* All paths departing from this node have been searched. Mark as
00257      * resolved if no cycles found. If cycles were found further cycles
00258      * could be found in this branch, thus it has to be searched again next
00259      * time we spot it.
00260      */
00261     path[next_id] = found ? NULL : invalid_path;
00262     return found;
00263   } else {
00264     /* this node has already been visited => we have a cycle
00265      * backtrack to find the exact flow
00266      */
00267     uint flow = this->FindCycleFlow(path, at_next_pos);
00268     if (flow > 0) {
00269       this->EliminateCycle(path, at_next_pos, flow);
00270       return true;
00271     } else {
00272       return false;
00273     }
00274   }
00275 }
00276 
00282 bool MCF1stPass::EliminateCycles()
00283 {
00284   bool cycles_found = false;
00285   uint size = this->graph->GetSize();
00286   PathVector path(size, NULL);
00287   for (NodeID node = 0; node < size; ++node) {
00288     /* starting at each node in the graph find all cycles involving this
00289      * node
00290      */
00291     std::fill(path.begin(), path.end(), (Path *)NULL);
00292     cycles_found |= this->EliminateCycles(path, node, node);
00293   }
00294   return cycles_found;
00295 }
00296 
00301 MCF1stPass::MCF1stPass(LinkGraphComponent *graph) : MultiCommodityFlow(graph)
00302 {
00303   PathVector paths;
00304   uint size = this->graph->GetSize();
00305   uint accuracy = this->graph->GetSettings().accuracy;
00306   bool more_loops = true;
00307 
00308   while (more_loops) {
00309     more_loops = false;
00310 
00311     for (NodeID source = 0; source < size; ++source) {
00312       /* first saturate the shortest paths */
00313       this->Dijkstra<DistanceAnnotation>(source, paths, true);
00314 
00315       for (NodeID dest = 0; dest < size; ++dest) {
00316         Edge &edge = this->graph->GetEdge(source, dest);
00317         if (edge.unsatisfied_demand > 0) {
00318           Path *path = paths[dest];
00319           assert(path != NULL);
00320           /* generally only allow paths that don't exceed the
00321            * available capacity. But if no demand has been assigned
00322            * yet, make an exception and allow any valid path *once*.
00323            */
00324           if (path->GetFreeCapacity() > 0 && this->PushFlow(edge, path,
00325               accuracy, true) > 0) {
00326             /* if a path has been found there is a chance we can
00327              * find more
00328              */
00329             more_loops = (edge.unsatisfied_demand > 0);
00330           } else if (edge.unsatisfied_demand == edge.demand &&
00331               path->GetFreeCapacity() > INT_MIN) {
00332             this->PushFlow(edge, path, accuracy, false);
00333           }
00334         }
00335       }
00336       this->CleanupPaths(source, paths);
00337     }
00338     if (!more_loops) more_loops = this->EliminateCycles();
00339   }
00340 }
00341 
00347 MCF2ndPass::MCF2ndPass(LinkGraphComponent *graph) : MultiCommodityFlow(graph)
00348 {
00349   PathVector paths;
00350   uint size = this->graph->GetSize();
00351   uint accuracy = this->graph->GetSettings().accuracy;
00352   bool demand_left = true;
00353   while (demand_left) {
00354     demand_left = false;
00355     for (NodeID source = 0; source < size; ++source) {
00356       this->Dijkstra<CapacityAnnotation>(source, paths, false);
00357       for (NodeID dest = 0; dest < size; ++dest) {
00358         Edge &edge = this->graph->GetEdge(source, dest);
00359         Path *path = paths[dest];
00360         if (edge.unsatisfied_demand > 0 && path->GetFreeCapacity() > INT_MIN) {
00361           this->PushFlow(edge, path, accuracy, false);
00362           if (edge.unsatisfied_demand > 0) demand_left = true;
00363         }
00364       }
00365       this->CleanupPaths(source, paths);
00366     }
00367   }
00368 }
00369 
00381 template <typename T>
00382 bool greater(T x_anno, T y_anno, NodeID x, NodeID y)
00383 {
00384   if (x_anno > y_anno) {
00385     return true;
00386   } else if (x_anno < y_anno) {
00387     return false;
00388   } else {
00389     return x > y;
00390   }
00391 }
00392 
00399 bool CapacityAnnotation::Comparator::operator()(const CapacityAnnotation *x,
00400     const CapacityAnnotation *y) const
00401 {
00402   return x != y && greater<int>(x->GetAnnotation(), y->GetAnnotation(),
00403       x->GetNode(), y->GetNode());
00404 }
00405 
00412 bool DistanceAnnotation::Comparator::operator()(const DistanceAnnotation *x,
00413     const DistanceAnnotation *y) const
00414 {
00415   return x != y && !greater<uint>(x->GetAnnotation(), y->GetAnnotation(),
00416       x->GetNode(), y->GetNode());
00417 }

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