public Map<RouteDirectionStopKey, String> getStopMatches(
      Map<NBRoute, Route> routeMatches,
      Map<NBStop, List<Stop>> potentialStopMatches,
      GtfsRelationalDao dao) {

    Map<RouteDirectionStopKey, String> stopIdMappings =
        new HashMap<RouteDirectionStopKey, String>();

    for (Map.Entry<NBRoute, Route> entry : routeMatches.entrySet()) {

      NBRoute nbRoute = entry.getKey();
      Route gtfsRoute = entry.getValue();

      Set<List<Stop>> stopSequences = getStopSequencesForRoute(dao, gtfsRoute);

      List<Map<Stop, Integer>> stopSequenceIndices = new ArrayList<Map<Stop, Integer>>();
      for (List<Stop> stopSequence : stopSequences) {
        Map<Stop, Integer> index = new HashMap<Stop, Integer>();
        for (int i = 0; i < stopSequence.size(); ++i) {
          index.put(stopSequence.get(i), i);
        }
        stopSequenceIndices.add(index);
      }

      for (NBDirection direction : nbRoute.getDirections()) {

        List<Match> matches = new ArrayList<Match>();
        for (NBStop fromStop : direction.getStops()) {
          List<Stop> toStops = potentialStopMatches.get(fromStop);
          if (toStops.isEmpty()) {
            continue;
          }
          Match m = new Match(fromStop, toStops);
          matches.add(m);
        }

        Min<Assignment> m = new Min<Assignment>();
        Assignment assignment = new Assignment(direction.getStops(), stopSequenceIndices);
        matches = applyDirectMatchesToAssignment(matches, assignment);
        recursivelyBuildAndScoreAssignment(matches, 0, assignment, m);
        Assignment bestAssignment = m.getMinElement();

        if (bestAssignment == null) {
          throw new IllegalStateException();
        }

        for (NBStop stop : direction.getStops()) {
          Stop gtfsStop = bestAssignment.getGtfsStopForNBStop(stop);
          if (gtfsStop == null) {
            continue;
          }
          String stopId = gtfsStop.getId().getId();
          RouteDirectionStopKey key =
              new RouteDirectionStopKey(nbRoute.getTag(), direction.getTag(), stop.getTag());
          stopIdMappings.put(key, stopId);
        }
      }
    }
    return stopIdMappings;
  }
  private void recursivelyBuildAndScoreAssignment(
      List<Match> matches, int depth, Assignment assignment, Min<Assignment> m) {
    if (depth == matches.size()) {
      double score = scoreAssignment(assignment);
      if (score < m.getMinValue()) {
        m.add(score, new Assignment(assignment));
      }

    } else {
      Match match = matches.get(depth);
      for (int i = 0; i < match.to.size(); ++i) {
        assignment.applyMatch(match, i);
        recursivelyBuildAndScoreAssignment(matches, depth + 1, assignment, m);
      }
    }
  }