mcf.cpp

Go to the documentation of this file.

 
#include "../stdafx.h"
#include "../core/math_func.hpp"
#include "../timer/timer_game_tick.h"
#include "mcf.h"
 
#include "../safeguards.h"
 
typedef std::map<NodeID, Path *> PathViaMap;
 
class DistanceAnnotation : public Path {
public:
 
  DistanceAnnotation(NodeID n, bool source = false) : Path(n, source) {}
 
  bool IsBetter(const DistanceAnnotation *base, uint cap, int free_cap, uint dist) const;
 
  inline uint GetAnnotation() const { return this->distance; }
 
  inline void UpdateAnnotation() { }
 
  struct Comparator {
    bool operator()(const DistanceAnnotation *x, const DistanceAnnotation *y) const;
  };
};
 
class CapacityAnnotation : public Path {
  int cached_annotation;
 
public:
 
  CapacityAnnotation(NodeID n, bool source = false) : Path(n, source) {}
 
  bool IsBetter(const CapacityAnnotation *base, uint cap, int free_cap, uint dist) const;
 
  inline int GetAnnotation() const { return this->cached_annotation; }
 
  inline void UpdateAnnotation()
  {
    this->cached_annotation = this->GetCapacityRatio();
  }
 
  struct Comparator {
    bool operator()(const CapacityAnnotation *x, const CapacityAnnotation *y) const;
  };
};
 
class GraphEdgeIterator {
private:
  LinkGraphJob &job; 
 
  std::vector<LinkGraphJob::EdgeAnnotation>::const_iterator i;   
  std::vector<LinkGraphJob::EdgeAnnotation>::const_iterator end; 
 
public:
 
  GraphEdgeIterator(LinkGraphJob &job) : job(job), i(), end() {}
 
  void SetNode(NodeID, NodeID node)
  {
    this->i = this->job[node].edges.cbegin();
    this->end = this->job[node].edges.cend();
  }
 
  NodeID Next()
  {
    return this->i != this->end ? (this->i++)->base.dest_node : INVALID_NODE;
  }
};
 
class FlowEdgeIterator {
private:
  LinkGraphJob &job; 
 
  std::vector<NodeID> station_to_node;
 
  FlowStat::SharesMap::const_iterator it;
 
  FlowStat::SharesMap::const_iterator end;
public:
 
  FlowEdgeIterator(LinkGraphJob &job) : job(job)
  {
    for (NodeID i = 0; i < job.Size(); ++i) {
      StationID st = job[i].base.station;
      if (st >= this->station_to_node.size()) {
        this->station_to_node.resize(st + 1);
      }
      this->station_to_node[st] = i;
    }
  }
 
  void SetNode(NodeID source, NodeID node)
  {
    const FlowStatMap &flows = this->job[node].flows;
    FlowStatMap::const_iterator it = flows.find(this->job[source].base.station);
    if (it != flows.end()) {
      this->it = it->second.GetShares()->begin();
      this->end = it->second.GetShares()->end();
    } else {
      this->it = FlowStat::empty_sharesmap.begin();
      this->end = FlowStat::empty_sharesmap.end();
    }
  }
 
  NodeID Next()
  {
    if (this->it == this->end) return INVALID_NODE;
    return this->station_to_node[(this->it++)->second];
  }
};
 
bool DistanceAnnotation::IsBetter(const DistanceAnnotation *base, uint,
    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);
  }
}
 
bool CapacityAnnotation::IsBetter(const CapacityAnnotation *base, uint cap,
    int free_cap, uint dist) const
{
  int min_cap = Path::GetCapacityRatio(std::min(base->free_capacity, free_cap), std::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;
  }
}
 
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);
  uint16_t size = this->job.Size();
  AnnoSet annos;
  paths.resize(size, nullptr);
  for (NodeID node = 0; node < size; ++node) {
    Tannotation *anno = new Tannotation(node, node == source_node);
    anno->UpdateAnnotation();
    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.
      const Edge &edge = this->job[from][to];
      uint capacity = edge.base.capacity;
      if (this->max_saturation != UINT_MAX) {
        capacity *= this->max_saturation;
        capacity /= 100;
        if (capacity == 0) capacity = 1;
      }
      /* Prioritize the fastest route for passengers, mail and express cargo,
       * and the shortest route for other classes of cargo.
       * In-between stops are punished with a 1 tile or 1 day penalty. */
      bool express = IsCargoInClass(this->job.Cargo(), CC_PASSENGERS) ||
        IsCargoInClass(this->job.Cargo(), CC_MAIL) ||
        IsCargoInClass(this->job.Cargo(), CC_EXPRESS);
      uint distance = DistanceMaxPlusManhattan(this->job[from].base.xy, this->job[to].base.xy) + 1;
      /* Compute a default travel time from the distance and an average speed of 1 tile/day. */
      uint time = (edge.base.TravelTime() != 0) ? edge.base.TravelTime() + Ticks::DAY_TICKS : distance * Ticks::DAY_TICKS;
      uint distance_anno = express ? time : distance;
 
      Tannotation *dest = static_cast<Tannotation *>(paths[to]);
      if (dest->IsBetter(source, capacity, capacity - edge.Flow(), distance_anno)) {
        annos.erase(dest);
        dest->Fork(source, capacity, capacity - edge.Flow(), distance_anno);
        dest->UpdateAnnotation();
        annos.insert(dest);
      }
    }
  }
}
 
void MultiCommodityFlow::CleanupPaths(NodeID source_id, PathVector &paths)
{
  Path *source = paths[source_id];
  paths[source_id] = nullptr;
  for (PathVector::iterator i = paths.begin(); i != paths.end(); ++i) {
    Path *path = *i;
    if (path == nullptr) continue;
    if (path->GetParent() == source) path->Detach();
    while (path != source && path != nullptr && path->GetFlow() == 0) {
      Path *parent = path->GetParent();
      path->Detach();
      if (path->GetNumChildren() == 0) {
        paths[path->GetNode()] = nullptr;
        delete path;
      }
      path = parent;
    }
  }
  delete source;
  paths.clear();
}
 
uint MultiCommodityFlow::PushFlow(Node &node, NodeID to, Path *path, uint accuracy,
    uint max_saturation)
{
  assert(node.UnsatisfiedDemandTo(to) > 0);
  uint flow = Clamp(node.DemandTo(to) / accuracy, 1, node.UnsatisfiedDemandTo(to));
  flow = path->AddFlow(flow, this->job, max_saturation);
  node.SatisfyDemandTo(to, flow);
  return flow;
}
 
uint MCF1stPass::FindCycleFlow(const PathVector &path, const Path *cycle_begin)
{
  uint flow = UINT_MAX;
  const Path *cycle_end = cycle_begin;
  do {
    flow = std::min(flow, cycle_begin->GetFlow());
    cycle_begin = path[cycle_begin->GetNode()];
  } while (cycle_begin != cycle_end);
  return flow;
}
 
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);
}
 
bool MCF1stPass::EliminateCycles(PathVector &path, NodeID origin_id, NodeID next_id)
{
  Path *at_next_pos = path[next_id];
 
  /* this node has already been searched */
  if (at_next_pos == Path::invalid_path) return false;
 
  if (at_next_pos == nullptr) {
    /* 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 ? nullptr : Path::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;
}
 
bool MCF1stPass::EliminateCycles()
{
  bool cycles_found = false;
  uint16_t size = this->job.Size();
  PathVector path(size, nullptr);
  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 *)nullptr);
    cycles_found |= this->EliminateCycles(path, node, node);
  }
  return cycles_found;
}
 
MCF1stPass::MCF1stPass(LinkGraphJob &job) : MultiCommodityFlow(job)
{
  PathVector paths;
  uint16_t size = job.Size();
  uint accuracy = job.Settings().accuracy;
  bool more_loops;
  std::vector<bool> finished_sources(size);
 
  do {
    more_loops = false;
    for (NodeID source = 0; source < size; ++source) {
      if (finished_sources[source]) continue;
 
      /* First saturate the shortest paths. */
      this->Dijkstra<DistanceAnnotation, GraphEdgeIterator>(source, paths);
 
      Node &src_node = job[source];
      bool source_demand_left = false;
      for (NodeID dest = 0; dest < size; ++dest) {
        if (src_node.UnsatisfiedDemandTo(dest) > 0) {
          Path *path = paths[dest];
          assert(path != nullptr);
          /* 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(src_node, dest, path,
              accuracy, this->max_saturation) > 0) {
            /* If a path has been found there is a chance we can
             * find more. */
            more_loops = more_loops || (src_node.UnsatisfiedDemandTo(dest) > 0);
          } else if (src_node.UnsatisfiedDemandTo(dest) == src_node.DemandTo(dest) &&
              path->GetFreeCapacity() > INT_MIN) {
            this->PushFlow(src_node, dest, path, accuracy, UINT_MAX);
          }
          if (src_node.UnsatisfiedDemandTo(dest) > 0) source_demand_left = true;
        }
      }
      finished_sources[source] = !source_demand_left;
      this->CleanupPaths(source, paths);
    }
  } while ((more_loops || this->EliminateCycles()) && !job.IsJobAborted());
}
 
MCF2ndPass::MCF2ndPass(LinkGraphJob &job) : MultiCommodityFlow(job)
{
  this->max_saturation = UINT_MAX; // disable artificial cap on saturation
  PathVector paths;
  uint16_t size = job.Size();
  uint accuracy = job.Settings().accuracy;
  bool demand_left = true;
  std::vector<bool> finished_sources(size);
  while (demand_left && !job.IsJobAborted()) {
    demand_left = false;
    for (NodeID source = 0; source < size; ++source) {
      if (finished_sources[source]) continue;
 
      this->Dijkstra<CapacityAnnotation, FlowEdgeIterator>(source, paths);
 
      Node &src_node = job[source];
      bool source_demand_left = false;
      for (NodeID dest = 0; dest < size; ++dest) {
        Path *path = paths[dest];
        if (src_node.UnsatisfiedDemandTo(dest) > 0 && path->GetFreeCapacity() > INT_MIN) {
          this->PushFlow(src_node, dest, path, accuracy, UINT_MAX);
          if (src_node.UnsatisfiedDemandTo(dest) > 0) {
            demand_left = true;
            source_demand_left = true;
          }
        }
      }
      finished_sources[source] = !source_demand_left;
      this->CleanupPaths(source, paths);
    }
  }
}
 
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;
}
 
bool CapacityAnnotation::Comparator::operator()(const CapacityAnnotation *x,
    const CapacityAnnotation *y) const
{
  return x != y && Greater<int>(x->GetAnnotation(), y->GetAnnotation(),
      x->GetNode(), y->GetNode());
}
 
bool DistanceAnnotation::Comparator::operator()(const DistanceAnnotation *x,
    const DistanceAnnotation *y) const
{
  return x != y && !Greater<uint>(x->GetAnnotation(), y->GetAnnotation(),
      x->GetNode(), y->GetNode());
}