include/fst/shortest-distance.h

// shortest-distance.h

// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Copyright 2005-2010 Google, Inc.
// Author: allauzen (at) google.com (Cyril Allauzen)
//
// \file
// Functions and classes to find shortest distance in an FST.

#ifndef FST_LIB_SHORTEST_DISTANCE_H__
#define FST_LIB_SHORTEST_DISTANCE_H__

#include <deque>
using std::deque;
#include <vector>
using std::vector;

#include <fst/arcfilter.h>
#include <fst/cache.h>
#include <fst/queue.h>
#include <fst/reverse.h>
#include <fst/test-properties.h>


namespace fst {

template <class Arc, class Queue, class ArcFilter>
struct ShortestDistanceOptions {
  typedef typename Arc::StateId StateId;

  Queue *state_queue;    // Queue discipline used; owned by caller
  ArcFilter arc_filter;  // Arc filter (e.g., limit to only epsilon graph)
  StateId source;        // If kNoStateId, use the Fst's initial state
  float delta;           // Determines the degree of convergence required
  bool first_path;       // For a semiring with the path property (o.w.
                         // undefined), compute the shortest-distances along
                         // along the first path to a final state found
                         // by the algorithm. That path is the shortest-path
                         // only if the FST has a unique final state (or all
                         // the final states have the same final weight), the
                         // queue discipline is shortest-first and all the
                         // weights in the FST are between One() and Zero()
                         // according to NaturalLess.

  ShortestDistanceOptions(Queue *q, ArcFilter filt, StateId src = kNoStateId,
                          float d = kDelta)
      : state_queue(q), arc_filter(filt), source(src), delta(d),
        first_path(false) {}
};


// Computation state of the shortest-distance algorithm. Reusable
// information is maintained across calls to member function
// ShortestDistance(source) when 'retain' is true for improved
// efficiency when calling multiple times from different source states
// (e.g., in epsilon removal). Contrary to usual conventions, 'fst'
// may not be freed before this class. Vector 'distance' should not be
// modified by the user between these calls.
// The Error() method returns true if an error was encountered.
template<class Arc, class Queue, class ArcFilter>
class ShortestDistanceState {
 public:
  typedef typename Arc::StateId StateId;
  typedef typename Arc::Weight Weight;

  ShortestDistanceState(
      const Fst<Arc> &fst,
      vector<Weight> *distance,
      const ShortestDistanceOptions<Arc, Queue, ArcFilter> &opts,
      bool retain)
      : fst_(fst), distance_(distance), state_queue_(opts.state_queue),
        arc_filter_(opts.arc_filter), delta_(opts.delta),
        first_path_(opts.first_path), retain_(retain), source_id_(0),
        error_(false) {
    distance_->clear();
  }

  ~ShortestDistanceState() {}

  void ShortestDistance(StateId source);

  bool Error() const { return error_; }

 private:
  const Fst<Arc> &fst_;
  vector<Weight> *distance_;
  Queue *state_queue_;
  ArcFilter arc_filter_;
  float delta_;
  bool first_path_;
  bool retain_;               // Retain and reuse information across calls

  vector<Weight> rdistance_;  // Relaxation distance.
  vector<bool> enqueued_;     // Is state enqueued?
  vector<StateId> sources_;   // Source ID for ith state in 'distance_',
                              //  'rdistance_', and 'enqueued_' if retained.
  StateId source_id_;         // Unique ID characterizing each call to SD

  bool error_;
};

// Compute the shortest distance. If 'source' is kNoStateId, use
// the initial state of the Fst.
template <class Arc, class Queue, class ArcFilter>
void ShortestDistanceState<Arc, Queue, ArcFilter>::ShortestDistance(
    StateId source) {
  if (fst_.Start() == kNoStateId) {
    if (fst_.Properties(kError, false)) error_ = true;
    return;
  }

  if (!(Weight::Properties() & kRightSemiring)) {
    FSTERROR() << "ShortestDistance: Weight needs to be right distributive: "
               << Weight::Type();
    error_ = true;
    return;
  }

  if (first_path_ && !(Weight::Properties() & kPath)) {
    FSTERROR() << "ShortestDistance: first_path option disallowed when "
               << "Weight does not have the path property: "
               << Weight::Type();
    error_ = true;
    return;
  }

  state_queue_->Clear();

  if (!retain_) {
    distance_->clear();
    rdistance_.clear();
    enqueued_.clear();
  }

  if (source == kNoStateId)
    source = fst_.Start();

  while (distance_->size() <= source) {
    distance_->push_back(Weight::Zero());
    rdistance_.push_back(Weight::Zero());
    enqueued_.push_back(false);
  }
  if (retain_) {
    while (sources_.size() <= source)
      sources_.push_back(kNoStateId);
    sources_[source] = source_id_;
  }
  (*distance_)[source] = Weight::One();
  rdistance_[source] = Weight::One();
  enqueued_[source] = true;

  state_queue_->Enqueue(source);

  while (!state_queue_->Empty()) {
    StateId s = state_queue_->Head();
    state_queue_->Dequeue();
    while (distance_->size() <= s) {
      distance_->push_back(Weight::Zero());
      rdistance_.push_back(Weight::Zero());
      enqueued_.push_back(false);
    }
    if (first_path_ && (fst_.Final(s) != Weight::Zero()))
      break;
    enqueued_[s] = false;
    Weight r = rdistance_[s];
    rdistance_[s] = Weight::Zero();
    for (ArcIterator< Fst<Arc> > aiter(fst_, s);
         !aiter.Done();
         aiter.Next()) {
      const Arc &arc = aiter.Value();
      if (!arc_filter_(arc))
        continue;
      while (distance_->size() <= arc.nextstate) {
        distance_->push_back(Weight::Zero());
        rdistance_.push_back(Weight::Zero());
        enqueued_.push_back(false);
      }
      if (retain_) {
        while (sources_.size() <= arc.nextstate)
          sources_.push_back(kNoStateId);
        if (sources_[arc.nextstate] != source_id_) {
          (*distance_)[arc.nextstate] = Weight::Zero();
          rdistance_[arc.nextstate] = Weight::Zero();
          enqueued_[arc.nextstate] = false;
          sources_[arc.nextstate] = source_id_;
        }
      }
      Weight &nd = (*distance_)[arc.nextstate];
      Weight &nr = rdistance_[arc.nextstate];
      Weight w = Times(r, arc.weight);
      if (!ApproxEqual(nd, Plus(nd, w), delta_)) {
        nd = Plus(nd, w);
        nr = Plus(nr, w);
        if (!nd.Member() || !nr.Member()) {
          error_ = true;
          return;
        }
        if (!enqueued_[arc.nextstate]) {
          state_queue_->Enqueue(arc.nextstate);
          enqueued_[arc.nextstate] = true;
        } else {
          state_queue_->Update(arc.nextstate);
        }
      }
    }
  }
  ++source_id_;
  if (fst_.Properties(kError, false)) error_ = true;
}


// Shortest-distance algorithm: this version allows fine control
// via the options argument. See below for a simpler interface.
//
// This computes the shortest distance from the 'opts.source' state to
// each visited state S and stores the value in the 'distance' vector.
// An unvisited state S has distance Zero(), which will be stored in
// the 'distance' vector if S is less than the maximum visited state.
// The state queue discipline, arc filter, and convergence delta are
// taken in the options argument.
// The 'distance' vector will contain a unique element for which
// Member() is false if an error was encountered.
//
// The weights must must be right distributive and k-closed (i.e., 1 +
// x + x^2 + ... + x^(k +1) = 1 + x + x^2 + ... + x^k).
//
// The algorithm is from Mohri, "Semiring Framweork and Algorithms for
// Shortest-Distance Problems", Journal of Automata, Languages and
// Combinatorics 7(3):321-350, 2002. The complexity of algorithm
// depends on the properties of the semiring and the queue discipline
// used. Refer to the paper for more details.
template<class Arc, class Queue, class ArcFilter>
void ShortestDistance(
    const Fst<Arc> &fst,
    vector<typename Arc::Weight> *distance,
    const ShortestDistanceOptions<Arc, Queue, ArcFilter> &opts) {

  ShortestDistanceState<Arc, Queue, ArcFilter>
    sd_state(fst, distance, opts, false);
  sd_state.ShortestDistance(opts.source);
  if (sd_state.Error()) {
    distance->clear();
    distance->resize(1, Arc::Weight::NoWeight());
  }
}

// Shortest-distance algorithm: simplified interface. See above for a
// version that allows finer control.
//
// If 'reverse' is false, this computes the shortest distance from the
// initial state to each state S and stores the value in the
// 'distance' vector. If 'reverse' is true, this computes the shortest
// distance from each state to the final states.  An unvisited state S
// has distance Zero(), which will be stored in the 'distance' vector
// if S is less than the maximum visited state.  The state queue
// discipline is automatically-selected.
// The 'distance' vector will contain a unique element for which
// Member() is false if an error was encountered.
//
// The weights must must be right (left) distributive if reverse is
// false (true) and k-closed (i.e., 1 + x + x^2 + ... + x^(k +1) = 1 +
// x + x^2 + ... + x^k).
//
// The algorithm is from Mohri, "Semiring Framweork and Algorithms for
// Shortest-Distance Problems", Journal of Automata, Languages and
// Combinatorics 7(3):321-350, 2002. The complexity of algorithm
// depends on the properties of the semiring and the queue discipline
// used. Refer to the paper for more details.
template<class Arc>
void ShortestDistance(const Fst<Arc> &fst,
                      vector<typename Arc::Weight> *distance,
                      bool reverse = false,
                      float delta = kDelta) {
  typedef typename Arc::StateId StateId;
  typedef typename Arc::Weight Weight;

  if (!reverse) {
    AnyArcFilter<Arc> arc_filter;
    AutoQueue<StateId> state_queue(fst, distance, arc_filter);
    ShortestDistanceOptions< Arc, AutoQueue<StateId>, AnyArcFilter<Arc> >
      opts(&state_queue, arc_filter);
    opts.delta = delta;
    ShortestDistance(fst, distance, opts);
  } else {
    typedef ReverseArc<Arc> ReverseArc;
    typedef typename ReverseArc::Weight ReverseWeight;
    AnyArcFilter<ReverseArc> rarc_filter;
    VectorFst<ReverseArc> rfst;
    Reverse(fst, &rfst);
    vector<ReverseWeight> rdistance;
    AutoQueue<StateId> state_queue(rfst, &rdistance, rarc_filter);
    ShortestDistanceOptions< ReverseArc, AutoQueue<StateId>,
      AnyArcFilter<ReverseArc> >
      ropts(&state_queue, rarc_filter);
    ropts.delta = delta;
    ShortestDistance(rfst, &rdistance, ropts);
    distance->clear();
    if (rdistance.size() == 1 && !rdistance[0].Member()) {
      distance->resize(1, Arc::Weight::NoWeight());
      return;
    }
    while (distance->size() < rdistance.size() - 1)
      distance->push_back(rdistance[distance->size() + 1].Reverse());
  }
}


// Return the sum of the weight of all successful paths in an FST, i.e.,
// the shortest-distance from the initial state to the final states.
// Returns a weight such that Member() is false if an error was encountered.
template <class Arc>
typename Arc::Weight ShortestDistance(const Fst<Arc> &fst, float delta = kDelta) {
  typedef typename Arc::Weight Weight;
  typedef typename Arc::StateId StateId;
  vector<Weight> distance;
  if (Weight::Properties() & kRightSemiring) {
    ShortestDistance(fst, &distance, false, delta);
    if (distance.size() == 1 && !distance[0].Member())
      return Arc::Weight::NoWeight();
    Weight sum = Weight::Zero();
    for (StateId s = 0; s < distance.size(); ++s)
      sum = Plus(sum, Times(distance[s], fst.Final(s)));
    return sum;
  } else {
    ShortestDistance(fst, &distance, true, delta);
    StateId s = fst.Start();
    if (distance.size() == 1 && !distance[0].Member())
      return Arc::Weight::NoWeight();
    return s != kNoStateId && s < distance.size() ?
        distance[s] : Weight::Zero();
  }
}


}  // namespace fst

#endif  // FST_LIB_SHORTEST_DISTANCE_H__