gum::StaticTriangulation Class Reference

base class for all non-incremental triangulation methods More...

#include <staticTriangulation.h>

Inheritance diagram for gum::StaticTriangulation:

Collaboration diagram for gum::StaticTriangulation:

Public Member Functions
Accessors / Modifiers
double	maxLog10CliqueDomainSize ()
	returns the max of log10DomainSize of the cliques in the junction tree. More...
const NodeProperty< Size > *	domainSizes () const
	returns the domain sizes of the variables of the graph to be triangulated More...

Protected Attributes
EliminationSequenceStrategy *	elimination_sequence_strategy_ {nullptr}
	the elimination sequence strategy used by the triangulation More...
JunctionTreeStrategy *	junction_tree_strategy_ {nullptr}
	the junction tree strategy used by the triangulation More...
const NodeProperty< Size > *	domain_sizes_ {nullptr}
	the domain sizes of the variables/nodes of the graph More...

Constructors / Destructors
virtual StaticTriangulation *	newFactory () const =0
	returns a fresh triangulation of the same type as the current object but over an empty graph More...
virtual StaticTriangulation *	copyFactory () const =0
	virtual copy constructor More...
virtual	~StaticTriangulation ()
	destructor More...
	StaticTriangulation (const EliminationSequenceStrategy &elimSeq, const JunctionTreeStrategy &JTStrategy, bool minimality=false)
	default constructor: without any graph More...
	StaticTriangulation (const UndiGraph *graph, const NodeProperty< Size > *dom_sizes, const EliminationSequenceStrategy &elimSeq, const JunctionTreeStrategy &JTStrategy, bool minimality=false)
	constructor with a given graph More...
	StaticTriangulation (const StaticTriangulation &)
	forbid copy constructor except in newfactory More...
	StaticTriangulation (StaticTriangulation &&)
	forbid move constructor except in children's constructors More...

Accessors / Modifiers
virtual void	setGraph (const UndiGraph *graph, const NodeProperty< Size > *domsizes)
	initialize the triangulation data structures for a new graph More...
const EdgeSet &	fillIns ()
	returns the fill-ins added by the triangulation algorithm More...
const std::vector< NodeId > &	eliminationOrder ()
	returns an elimination ordering compatible with the triangulated graph More...
Idx	eliminationOrder (const NodeId)
	returns the index of a given node in the elimination order (0 = first node eliminated) More...
const NodeProperty< NodeId > &	reverseEliminationOrder ()
	returns a table indicating, for each node, at which step it was deleted by the triangulation process More...
const UndiGraph &	triangulatedGraph ()
	returns the triangulated graph More...
const CliqueGraph &	eliminationTree ()
	returns the elimination tree of a compatible ordering More...
const CliqueGraph &	junctionTree ()
	returns a compatible junction tree More...
NodeId	createdJunctionTreeClique (const NodeId id)
	returns the Id of the clique of the junction tree created by the elimination of a given node during the triangulation process More...
const NodeProperty< NodeId > &	createdJunctionTreeCliques ()
	returns the Ids of the cliques of the junction tree created by the elimination of the nodes More...
const CliqueGraph &	maxPrimeSubgraphTree ()
	returns a junction tree of maximal prime subgraphs More...
NodeId	createdMaxPrimeSubgraph (const NodeId id)
	returns the Id of the maximal prime subgraph created by the elimination of a given node during the triangulation process More...
void	clear ()
	reinitialize the graph to be triangulated to an empty graph More...
void	setMinimalRequirement (bool)
	sets/unset the minimality requirement More...
virtual bool	isMinimalityRequired () const final
	indicates wether minimality is required More...
void	setFillIns (bool)
	sets/unsets the record of the fill-ins in the standard triangulation procedure More...
const UndiGraph *	originalGraph () const
	returns the graph to be triangulated More...
EliminationSequenceStrategy &	eliminationSequenceStrategy () const
	returns the elimination sequence strategy used by the triangulation More...
JunctionTreeStrategy &	junctionTreeStrategy () const
	returns the junction tree strategy used by the triangulation More...
virtual void	initTriangulation_ (UndiGraph &graph)
	the function called to initialize the triangulation process More...

Detailed Description

base class for all non-incremental triangulation methods

Definition at line 49 of file staticTriangulation.h.

Constructor & Destructor Documentation

~StaticTriangulation()

gum::StaticTriangulation::~StaticTriangulation ( )

virtual

destructor

Definition at line 142 of file staticTriangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                            {
    // for debugging purposes
    GUM_DESTRUCTOR(StaticTriangulation);

    delete elimination_sequence_strategy_;
    delete junction_tree_strategy_;

    // no need to deallocate  _original_graph_ nor  _junction_tree_ because
    // they are not owned by the static triangulation class
  }

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StaticTriangulation() [1/4]

gum::StaticTriangulation::StaticTriangulation ( const EliminationSequenceStrategy &  elimSeq, const JunctionTreeStrategy &  JTStrategy, bool  minimality = false  )

protected

default constructor: without any graph

Parameters

elimSeq	the elimination sequence used to triangulate the graph
JTStrategy	the junction tree strategy used to create junction trees from elimination trees
minimality	a Boolean indicating whether we should enforce that the triangulation is minimal w.r.t. inclusion

Definition at line 67 of file staticTriangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                                                          :
      elimination_sequence_strategy_(elimSeq.newFactory()),
      junction_tree_strategy_(JTStrategy.newFactory()), _minimality_required_(minimality) {
    // for debugging purposes
    GUM_CONSTRUCTOR(StaticTriangulation);

    // register the triangulation to its junction tree strategy
    junction_tree_strategy_->setTriangulation(this);
  }

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StaticTriangulation() [2/4]

gum::StaticTriangulation::StaticTriangulation ( const UndiGraph *  graph, const NodeProperty< Size > *  dom_sizes, const EliminationSequenceStrategy &  elimSeq, const JunctionTreeStrategy &  JTStrategy, bool  minimality = false  )

protected

constructor with a given graph

Parameters

graph	the graph to be triangulated, i.e., the nodes of which will be eliminated
dom_sizes	the domain sizes of the nodes to be eliminated
elimSeq	the elimination sequence used to triangulate the graph
JTStrategy	the junction tree strategy used to create junction trees

Warning

Note that we allow dom_sizes to be defined over nodes/variables that do not belong to graph. These sizes will simply be ignored. However, it is compulsory that all the nodes of graph belong to dom_sizes

Parameters

minimality

a Boolean indicating whether we should enforce that the triangulation is minimal w.r.t. inclusion

Warning

note that, by aGrUM's rule, the graph is not copied but only referenced by the triangulation algorithm.

Definition at line 40 of file staticTriangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                                                          :
      Triangulation(domsizes),
      elimination_sequence_strategy_(elimSeq.newFactory()),
      junction_tree_strategy_(JTStrategy.newFactory()), _original_graph_(theGraph),
      _minimality_required_(minimality) {
    // for debugging purposes
    GUM_CONSTRUCTOR(StaticTriangulation);

    // if the graph is not empty, resize several structures in order to speed-up
    // their fillings.
    if (theGraph != nullptr) {
      _elim_order_.resize(theGraph->size());
      _reverse_elim_order_.resize(theGraph->size());
      _elim_cliques_.resize(theGraph->size());
      _node_2_max_prime_clique_.resize(theGraph->size());
      _added_fill_ins_.resize(theGraph->size());
    }

    // register the triangulation to its junction tree strategy
    junction_tree_strategy_->setTriangulation(this);
  }

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StaticTriangulation() [3/4]

gum::StaticTriangulation::StaticTriangulation ( const StaticTriangulation &  from )

protected

forbid copy constructor except in newfactory

Definition at line 80 of file staticTriangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                                          :
      Triangulation(from), _original_graph_(from._original_graph_),
      _triangulated_graph_(from._triangulated_graph_), _fill_ins_(from._fill_ins_),
      _elim_order_(from._elim_order_), _reverse_elim_order_(from._reverse_elim_order_),
      _elim_cliques_(from._elim_cliques_), _elim_tree_(from._elim_tree_),
      _max_prime_junction_tree_(from._max_prime_junction_tree_),
      _node_2_max_prime_clique_(from._node_2_max_prime_clique_),
      _has_triangulation_(from._has_triangulation_),
      _has_triangulated_graph_(from._has_triangulated_graph_),
      _has_elimination_tree_(from._has_elimination_tree_),
      _has_junction_tree_(from._has_junction_tree_),
      _has_max_prime_junction_tree_(from._has_max_prime_junction_tree_),
      _has_fill_ins_(from._has_fill_ins_), _minimality_required_(from._minimality_required_),
      _added_fill_ins_(from._added_fill_ins_), _we_want_fill_ins_(from._we_want_fill_ins_) {
    // copy the strategies
    elimination_sequence_strategy_ = from.elimination_sequence_strategy_->copyFactory();
    junction_tree_strategy_        = from.junction_tree_strategy_->copyFactory(this);

    // if from has a junction tree, copy it
    if (from._junction_tree_ != nullptr) {
      _junction_tree_ = &(junction_tree_strategy_->junctionTree());
    }

    // for debugging purposes
    GUM_CONS_CPY(StaticTriangulation);
  }

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StaticTriangulation() [4/4]

gum::StaticTriangulation::StaticTriangulation ( StaticTriangulation &&  from )

protected

forbid move constructor except in children's constructors

Definition at line 108 of file staticTriangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                                     :
      Triangulation(std::move(from)),
      elimination_sequence_strategy_(from.elimination_sequence_strategy_),
      junction_tree_strategy_(from.junction_tree_strategy_),
      _original_graph_(from._original_graph_),
      _triangulated_graph_(std::move(from._triangulated_graph_)),
      _fill_ins_(std::move(from._fill_ins_)), _elim_order_(std::move(from._elim_order_)),
      _reverse_elim_order_(std::move(from._reverse_elim_order_)),
      _elim_cliques_(std::move(from._elim_cliques_)), _elim_tree_(std::move(from._elim_tree_)),
      _max_prime_junction_tree_(std::move(from._max_prime_junction_tree_)),
      _node_2_max_prime_clique_(std::move(from._node_2_max_prime_clique_)),
      _has_triangulation_(from._has_triangulation_),
      _has_triangulated_graph_(from._has_triangulated_graph_),
      _has_elimination_tree_(from._has_elimination_tree_),
      _has_junction_tree_(from._has_junction_tree_),
      _has_max_prime_junction_tree_(from._has_max_prime_junction_tree_),
      _has_fill_ins_(from._has_fill_ins_), _minimality_required_(from._minimality_required_),
      _added_fill_ins_(std::move(from._added_fill_ins_)),
      _we_want_fill_ins_(from._we_want_fill_ins_) {
    // move the factories contained in from
    from.elimination_sequence_strategy_ = new DefaultEliminationSequenceStrategy;
    from.junction_tree_strategy_        = new DefaultJunctionTreeStrategy;
    junction_tree_strategy_->moveTriangulation(this);

    // if from has a junction tree, copy it
    if (from._junction_tree_ != nullptr) {
      _junction_tree_ = &(junction_tree_strategy_->junctionTree());
    }

    // for debugging purposes
    GUM_CONS_MOV(StaticTriangulation);
  }

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Member Function Documentation

_computeEliminationTree_()

void gum::StaticTriangulation::_computeEliminationTree_ ( )

private

returns an elimination tree from a triangulated graph

Definition at line 322 of file staticTriangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                     {
    // if there already exists an elimination tree, no need to compute it again
    if (_has_elimination_tree_) return;

    // if the graph is not triangulated, triangulate it
    if (!_has_triangulation_) _triangulate_();

    // create the nodes of the elimination tree
    _elim_tree_.clear();

    Size size = Size(_elim_order_.size());
    for (NodeId i = NodeId(0); i < size; ++i)
      _elim_tree_.addNode(i, _elim_cliques_[_elim_order_[i]]);

    // create the edges of the elimination tree: join a node to the one in
    // its clique that is eliminated first
    for (NodeId i = NodeId(0); i < size; ++i) {
      NodeId         clique_i_creator = _elim_order_[i];
      const NodeSet& list_of_nodes    = _elim_cliques_[clique_i_creator];
      Idx            child            = _original_graph_->bound() + 1;

      for (const auto node: list_of_nodes) {
        Idx it_elim_step = _reverse_elim_order_[node];

        if ((node != clique_i_creator) && (child > it_elim_step)) child = it_elim_step;
      }

      if (child <= _original_graph_->bound()) {
        // WARNING: here, we assume that the nodes of the elimination tree are
        // indexed from 0 to n-1
        _elim_tree_.addEdge(i, child);
      }
    }

    _has_elimination_tree_ = true;
  }

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_computeMaxPrimeJunctionTree_()

void gum::StaticTriangulation::_computeMaxPrimeJunctionTree_ ( )

private

computes the junction tree of the maximal prime subgraphs

Definition at line 392 of file staticTriangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                          {
    // if there already exists a max prime junction tree, no need
    // to recompute it
    if (_has_max_prime_junction_tree_) return;

    // if there is no junction tree, create it
    if (!_has_junction_tree_) junctionTree();

    // the maximal prime subgraph join tree is created by aggregation of some
    // cliques. More precisely, when the separator between 2 cliques is not
    // complete in the original graph, then the two cliques must be merged.
    // Create a hashtable indicating which clique has been absorbed by some
    // other
    // clique.
    NodeProperty< NodeId > T_mpd_cliques(_junction_tree_->size());

    for (const auto clik: _junction_tree_->nodes())
      T_mpd_cliques.insert(clik, clik);

    // parse all the separators of the junction tree and test those that are not
    // complete in the orginal graph
    std::vector< Arc > merged_cliques;

    NodeSet mark;

    for (const auto clik: _junction_tree_->nodes())
      if (!mark.contains(clik)) _computeMaxPrimeMergings_(clik, clik, merged_cliques, mark);

    // compute the transitive closure of merged_cliques. This one will contain
    // pairs (X,Y) indicating that clique X must be merged with clique Y.
    // Actually clique X will be inserted into clique Y.
    for (unsigned int i = 0; i < merged_cliques.size(); ++i) {
      T_mpd_cliques[merged_cliques[i].tail()] = T_mpd_cliques[merged_cliques[i].head()];
    }

    // now we can create the max prime junction tree. First, create the cliques
    for (const auto& elt: T_mpd_cliques)
      if (elt.first == elt.second)
        _max_prime_junction_tree_.addNode(elt.second, _junction_tree_->clique(elt.second));

    // add to the cliques previously created the nodes of the cliques that were
    // merged into them
    for (const auto& elt: T_mpd_cliques)
      if (elt.first != elt.second)
        for (const auto node: _junction_tree_->clique(elt.first)) {
          try {
            _max_prime_junction_tree_.addToClique(elt.second, node);
          } catch (DuplicateElement&) {}
        }

    // add the edges to the graph
    for (const auto& edge: _junction_tree_->edges()) {
      NodeId node1 = T_mpd_cliques[edge.first()];
      NodeId node2 = T_mpd_cliques[edge.second()];

      if (node1 != node2) {
        try {
          _max_prime_junction_tree_.addEdge(node1, node2);
        } catch (DuplicateElement&) {}
      }
    }

    // compute for each node which clique of the max prime junction tree was
    // created by the elimination of the node
    const NodeProperty< NodeId >& node_2_junction_clique
       = junction_tree_strategy_->createdCliques();

    for (const auto& elt: node_2_junction_clique)
      _node_2_max_prime_clique_.insert(elt.first, T_mpd_cliques[elt.second]);

    _has_max_prime_junction_tree_ = true;
  }

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_computeMaxPrimeMergings_()

void gum::StaticTriangulation::_computeMaxPrimeMergings_ ( const NodeId  node, const NodeId  from, std::vector< Arc > &  merged_cliques, NodeSet &  mark  ) const

private

used for computing the junction tree of the maximal prime subgraphs

Definition at line 360 of file staticTriangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                                                      {
    mark << node;

    for (const auto other_node: _junction_tree_->neighbours(node))
      if (other_node != from) {
        const NodeSet& separator = _junction_tree_->separator(node, other_node);
        // check that the separator between node and other_node is complete
        bool complete = true;

        for (auto iter_sep1 = separator.begin(); iter_sep1 != separator.end() && complete;
             ++iter_sep1) {
          auto iter_sep2 = iter_sep1;

          for (++iter_sep2; iter_sep2 != separator.end(); ++iter_sep2) {
            if (!_original_graph_->existsEdge(*iter_sep1, *iter_sep2)) {
              complete = false;
              break;
            }
          }
        }

        // here complete indicates whether the separator is complete or not
        if (!complete) merged_cliques.push_back(Arc(other_node, node));

        _computeMaxPrimeMergings_(other_node, node, merged_cliques, mark);
      }
  }

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_computeRecursiveThinning_()

void gum::StaticTriangulation::_computeRecursiveThinning_ ( )

private

removes redondant fill-ins and compute proper elimination cliques and order

Definition at line 184 of file staticTriangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                       {
    // apply recursive thinning (fmint, see Kjaerulff (90), "triangulation of
    // graphs - algorithms giving small total state space")
    NodeId                       node1, node2;
    bool                         incomplete;
    std::vector< NodeId >        adj;
    EdgeSet                      T_prime;
    NodeProperty< unsigned int > R(_triangulated_graph_.size());

    for (const auto node: _triangulated_graph_)
      R.insert(node, 0);

    // the FMINT loop
    if (_added_fill_ins_.size() > 0) {
      for (auto iter = _added_fill_ins_.rbegin(); iter != _added_fill_ins_.rend(); ++iter) {
        if (iter->size()) {
          // here apply MINT to T_i =  _added_fill_ins_[i]
          EdgeSet& T = *iter;

          // compute R: by default, R is equal to all the nodes in the graph
          // when R[...] >= j (see the j in the loop below), this means that the
          // node belongs to an extremal edge in R
          for (std::size_t k = 0; k < _elim_order_.size(); ++k)
            R[_elim_order_[k]] = 0;   // WARNING: do not replace R[ _elim_order_[k]] by

          // R[k] because the node ids may not be
          // consecutive numbers

          // apply MINT while some edges can possibly be deleted
          bool require_mint = true;

          for (unsigned int j = 0; require_mint; ++j) {
            // find T' (it is equal to the edges (v,w) of T such that
            // the intersection of adj(v,G) and adj(w,G) is complete and such
            // that
            // v and/or w belongs to an extremal node in R
            for (const auto& edge: T) {
              node1 = edge.first();
              node2 = edge.second();

              // check if at least one extremal node belongs to R
              if ((R[node1] < j) && (R[node2] < j)) continue;

              // check if the intersection of adj(v,G) and adj(w,G) is a
              // complete subgraph
              if (_triangulated_graph_.neighbours(node2).size()
                  < _triangulated_graph_.neighbours(node1).size()) {
                NodeId tmp = node1;
                node1      = node2;
                node2      = tmp;
              }

              incomplete = false;

              // find the nodes belonging to the intersection of adj(v,G)
              // and adj(w,G)
              for (const auto adjnode: _triangulated_graph_.neighbours(node1))
                if (_triangulated_graph_.existsEdge(node2, adjnode)) adj.push_back(adjnode);

              // check if the intersection is complete
              for (unsigned int k = 0; k < adj.size() && !incomplete; ++k) {
                for (unsigned int m = k + 1; m < adj.size(); ++m) {
                  if (!_triangulated_graph_.existsEdge(adj[k], adj[m])) {
                    incomplete = true;
                    break;
                  }
                }
              }

              adj.clear();

              if (!incomplete) {
                T_prime.insert(edge);
                R[node1] = j + 1;
                R[node2] = j + 1;
              }
            }

            // compute the new value of T (i.e. T\T') and update the
            // triangulated graph
            for (const auto& edge: T_prime) {
              T.erase(edge);
              _triangulated_graph_.eraseEdge(edge);

              if (_has_fill_ins_) _fill_ins_.erase(edge);
            }

            if (T_prime.size() == 0) require_mint = false;

            T_prime.clear();
          }
        }
      }
    }

    // here, the recursive thinning has removed all the superfluous edges.
    // Hence some cliques have been split and, as a result, the elimination
    // order has changed. We should thus compute a new perfect ordering. To
    // do so, we use a Maximal Cardinality Search: it has indeed the nice
    // property that, when the graph is already triangulated, it finds a
    // compatible order of elimination that does not require any edge addition

    // a structure storing the number of neighbours previously processed
    PriorityQueue< NodeId, unsigned int, std::greater< unsigned int > > numbered_neighbours(
       std::greater< unsigned int >(),
       _triangulated_graph_.size());

    for (Size i = 0; i < _elim_order_.size(); ++i)
      numbered_neighbours.insert(_elim_order_[i], 0);

    // perform the maximum cardinality search
    if (_elim_order_.size() > 0) {
      for (Size i = Size(_elim_order_.size()); i >= 1; --i) {
        NodeId ni                  = NodeId(i - 1);
        NodeId node                = numbered_neighbours.pop();
        _elim_order_[ni]           = node;
        _reverse_elim_order_[node] = ni;

        for (const auto neighbour: _triangulated_graph_.neighbours(node)) {
          try {
            numbered_neighbours.setPriority(neighbour, 1 + numbered_neighbours.priority(neighbour));
          } catch (NotFound&) {}
        }
      }
    }

    // here the elimination order is ok. We now need to update the
    //  _elim_cliques_
    for (Size i = 0; i < _elim_order_.size(); ++i) {
      NodeSet& cliques = _elim_cliques_.insert(_elim_order_[i], NodeSet()).second;
      cliques << _elim_order_[i];

      for (const auto neighbour: _triangulated_graph_.neighbours(_elim_order_[i]))
        if (_reverse_elim_order_[neighbour] > i) cliques << neighbour;
    }
  }

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_triangulate_()

void gum::StaticTriangulation::_triangulate_ ( )

private

the function that performs the triangulation

Definition at line 532 of file staticTriangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                          {
    // if the graph is already triangulated, no need to triangulate it again
    if (_has_triangulation_) return;

    // copy the graph to be triangulated, so that we can modify it
    UndiGraph tmp_graph = *_original_graph_;

    initTriangulation_(tmp_graph);
    elimination_sequence_strategy_->askFillIns(_we_want_fill_ins_);

    // if we are to do recursive thinning, we will have to add fill-ins to the
    // triangulated graph each time we eliminate a node. Hence, we shall
    // initialize the triangulated graph by a copy of the original graph
    if (_minimality_required_) {
      _triangulated_graph_     = *_original_graph_;
      _has_triangulated_graph_ = true;
    }

    // perform the triangulation
    NodeId removable_node = 0;

    for (unsigned int nb_elim = 0; tmp_graph.size() != 0; ++nb_elim) {
      removable_node = elimination_sequence_strategy_->nextNodeToEliminate();

      // when minimality is not required, i.e., we won't apply recursive
      // thinning, the cliques sets can be computed
      if (!_minimality_required_) {
        NodeSet& cliques = _elim_cliques_.insert(removable_node, NodeSet()).second;
        cliques.resize(tmp_graph.neighbours(removable_node).size() / 2);
        cliques << removable_node;
        for (const auto clik: tmp_graph.neighbours(removable_node))
          cliques << clik;
      } else {
        // here recursive thinning will be applied, hence we need store the
        // fill-ins added by the current node removal
        EdgeSet& current_fill = _added_fill_ins_[nb_elim];
        NodeId   node1, node2;

        const NodeSet& nei = tmp_graph.neighbours(removable_node);

        for (auto iter_edges1 = nei.begin(); iter_edges1 != nei.end(); ++iter_edges1) {
          node1            = *iter_edges1;
          auto iter_edges2 = iter_edges1;

          for (++iter_edges2; iter_edges2 != nei.end(); ++iter_edges2) {
            node2 = *iter_edges2;
            Edge edge(node1, node2);

            if (!tmp_graph.existsEdge(edge)) {
              current_fill.insert(edge);
              _triangulated_graph_.addEdge(node1, node2);
            }
          }
        }
      }

      // if we want fill-ins but the elimination sequence strategy does not
      // compute them, we shall compute them here
      if (_we_want_fill_ins_ && !elimination_sequence_strategy_->providesFillIns()) {
        NodeId node1, node2;

        // add edges between removable_node's neighbours in order to create
        // a clique
        const NodeSet& nei = tmp_graph.neighbours(removable_node);

        for (auto iter_edges1 = nei.begin(); iter_edges1 != nei.end(); ++iter_edges1) {
          node1            = *iter_edges1;
          auto iter_edges2 = iter_edges1;

          for (++iter_edges2; iter_edges2 != nei.end(); ++iter_edges2) {
            node2 = *iter_edges2;
            Edge edge(node1, node2);

            if (!tmp_graph.existsEdge(edge)) { _fill_ins_.insert(edge); }
          }
        }

        // delete removable_node and its adjacent edges
        tmp_graph.eraseNode(removable_node);
      }

      // inform the elimination sequence that we are actually removing
      // removable_node (this enables, for instance, to update the weights of
      // the nodes in the graph)
      elimination_sequence_strategy_->eliminationUpdate(removable_node);

      if (!elimination_sequence_strategy_->providesGraphUpdate()) {
        NodeId node1, node2;

        const NodeSet& nei = tmp_graph.neighbours(removable_node);

        for (auto iter_edges1 = nei.begin(); iter_edges1 != nei.end(); ++iter_edges1) {
          node1            = *iter_edges1;
          auto iter_edges2 = iter_edges1;

          for (++iter_edges2; iter_edges2 != nei.end(); ++iter_edges2) {
            node2 = *iter_edges2;
            Edge edge(node1, node2);

            if (!tmp_graph.existsEdge(edge)) { tmp_graph.addEdge(node1, node2); }
          }
        }

        tmp_graph.eraseNode(removable_node);
      }

      // update the elimination order
      _elim_order_[nb_elim] = removable_node;
      _reverse_elim_order_.insert(removable_node, nb_elim);
    }

    // indicate whether we actually computed fill-ins
    _has_fill_ins_ = _we_want_fill_ins_;

    // if minimality is required, remove the redondant edges
    if (_minimality_required_) _computeRecursiveThinning_();

    _has_triangulation_ = true;
  }

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clear()

void gum::StaticTriangulation::clear ( )

virtual

reinitialize the graph to be triangulated to an empty graph

Implements gum::Triangulation.

Definition at line 154 of file staticTriangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                  {
    // clear the factories
    elimination_sequence_strategy_->clear();
    junction_tree_strategy_->clear();

    // remove the current graphs
    _original_graph_ = nullptr;
    _junction_tree_  = nullptr;
    _triangulated_graph_.clear();
    _elim_tree_.clear();
    _max_prime_junction_tree_.clear();
    _elim_cliques_.clear();
    _node_2_max_prime_clique_.clear();

    // remove all fill-ins and orderings
    _fill_ins_.clear();
    _added_fill_ins_.clear();
    _elim_order_.clear();
    _reverse_elim_order_.clear();

    // indicates that the junction tree, the max prime tree, etc, are updated
    _has_triangulation_           = true;
    _has_triangulated_graph_      = true;
    _has_elimination_tree_        = true;
    _has_junction_tree_           = true;
    _has_max_prime_junction_tree_ = true;
    _has_fill_ins_                = true;
  }

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copyFactory()

virtual StaticTriangulation* gum::StaticTriangulation::copyFactory ( ) const

pure virtual

virtual copy constructor

note that we return a pointer as it enables subclasses to return pointers to their types, not Triangulation pointers. See item 25 of the more effective C++.

Implements gum::Triangulation.

Implemented in gum::PartialOrderedTriangulation, gum::OrderedTriangulation, gum::DefaultTriangulation, and gum::UnconstrainedTriangulation.

createdJunctionTreeClique()

NodeId gum::StaticTriangulation::createdJunctionTreeClique ( const NodeId  id )

virtual

returns the Id of the clique of the junction tree created by the elimination of a given node during the triangulation process

Implements gum::Triangulation.

createdJunctionTreeCliques()

const NodeProperty< NodeId >& gum::StaticTriangulation::createdJunctionTreeCliques ( )

virtual

returns the Ids of the cliques of the junction tree created by the elimination of the nodes

Implements gum::Triangulation.

createdMaxPrimeSubgraph()

NodeId gum::StaticTriangulation::createdMaxPrimeSubgraph ( const NodeId  id )

virtual

returns the Id of the maximal prime subgraph created by the elimination of a given node during the triangulation process

Implements gum::Triangulation.

domainSizes()

const NodeProperty< Size >* gum::Triangulation::domainSizes ( ) const

inherited

returns the domain sizes of the variables of the graph to be triangulated

eliminationOrder() [1/2]

const std::vector< NodeId >& gum::StaticTriangulation::eliminationOrder ( )

virtual

returns an elimination ordering compatible with the triangulated graph

Implements gum::Triangulation.

eliminationOrder() [2/2]

Idx gum::StaticTriangulation::eliminationOrder ( const NodeId  )

virtual

returns the index of a given node in the elimination order (0 = first node eliminated)

Implements gum::Triangulation.

eliminationSequenceStrategy()

EliminationSequenceStrategy& gum::StaticTriangulation::eliminationSequenceStrategy

(

)

const

returns the elimination sequence strategy used by the triangulation

eliminationTree()

const CliqueGraph& gum::StaticTriangulation::eliminationTree ( )

virtual

returns the elimination tree of a compatible ordering

Implements gum::Triangulation.

fillIns()

const EdgeSet & gum::StaticTriangulation::fillIns ( )

virtual

returns the fill-ins added by the triangulation algorithm

Implements gum::Triangulation.

Definition at line 653 of file staticTriangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                              {
    // if we did not compute the triangulation yet, do it and commpute
    // the fill-ins at the same time
    if (!_has_triangulation_) {
      bool want_fill_ins = _we_want_fill_ins_;
      _we_want_fill_ins_ = true;
      _triangulate_();
      _we_want_fill_ins_ = want_fill_ins;
      _has_fill_ins_     = true;
    }

    // here, we already computed a triangulation and we already computed
    // the fill-ins, so return them
    if (_has_fill_ins_) {
      if (elimination_sequence_strategy_->providesFillIns())
        return elimination_sequence_strategy_->fillIns();
      else
        return _fill_ins_;
    } else {
      // ok, here, we shall compute the fill-ins as they were not precomputed
      if (!_original_graph_) return _fill_ins_;

      // just in case, be sure that the junction tree has been constructed
      if (!_has_junction_tree_) junctionTree();

      for (const auto clik_id: _junction_tree_->nodes()) {
        // for each clique, add the edges necessary to make it complete
        const NodeSet&        clique = _junction_tree_->clique(clik_id);
        std::vector< NodeId > clique_nodes(clique.size());
        unsigned int          i = 0;

        for (const auto node: clique) {
          clique_nodes[i] = node;
          i += 1;
        }

        for (i = 0; i < clique_nodes.size(); ++i) {
          for (unsigned int j = i + 1; j < clique_nodes.size(); ++j) {
            Edge edge(clique_nodes[i], clique_nodes[j]);

            if (!_original_graph_->existsEdge(edge)) {
              try {
                _fill_ins_.insert(edge);
              } catch (DuplicateElement&) {}
            }
          }
        }
      }

      return _fill_ins_;
    }
  }

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initTriangulation_()

void gum::StaticTriangulation::initTriangulation_ ( UndiGraph &  graph )

protectedvirtual

the function called to initialize the triangulation process

This function is called when the triangulation process starts and is used to initialize the elimination sequence strategy. Actually, the graph that is modified by the triangulation algorithm is a copy of the original graph, and this copy needs be known by the elimination sequence strategy. initTriangulation_ is used to transmit this knowledge to the elimination sequence (through method setGraph of the elimination sequence class).

Parameters

graph

the very graph that is triangulated (this is a copy of original_graph)

Reimplemented in gum::PartialOrderedTriangulation, and gum::OrderedTriangulation.

Definition at line 707 of file staticTriangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                               {
    elimination_sequence_strategy_->setGraph(&graph, domain_sizes_);
  }

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isMinimalityRequired()

virtual bool gum::StaticTriangulation::isMinimalityRequired ( ) const

finalvirtual

indicates wether minimality is required

junctionTree()

const CliqueGraph& gum::StaticTriangulation::junctionTree ( )

virtual

returns a compatible junction tree

Implements gum::Triangulation.

junctionTreeStrategy()

JunctionTreeStrategy& gum::StaticTriangulation::junctionTreeStrategy

(

)

const

returns the junction tree strategy used by the triangulation

maxLog10CliqueDomainSize()

double gum::Triangulation::maxLog10CliqueDomainSize ( )

inherited

returns the max of log10DomainSize of the cliques in the junction tree.

This is usefull for instance to estimate the complexity (both in space and in time) of the inference that will use the junction tree.

This method is not 'const' since it can be called before building any junction tree and hence it needs to build it...

Definition at line 64 of file triangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                 {
    double              res = 0.0;
    double              dSize;
    const JunctionTree& jt = junctionTree();   // here, the fact that we get
    // a junction tree ensures that domain_sizes_ is different from nullptr

    for (const NodeId cl: jt) {
      dSize = 0.0;

      for (const auto node: jt.clique(cl))
        dSize += std::log10((*domain_sizes_)[node]);

      if (res < dSize) res = dSize;
    }

    return res;
  }

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maxPrimeSubgraphTree()

const CliqueGraph& gum::StaticTriangulation::maxPrimeSubgraphTree ( )

virtual

returns a junction tree of maximal prime subgraphs

Warning

Actually, the cliques of the junction tree are guarranteed to be maximal prime subgraph of the original graph that was triangulated only if the triangulation performed is minimal (in the sense that removing any edge in the triangulated graph results in a nontriangulated graph). This can be ensured by requiring minimality of the triangulation.

Implements gum::Triangulation.

newFactory()

virtual StaticTriangulation* gum::StaticTriangulation::newFactory ( ) const

pure virtual

returns a fresh triangulation of the same type as the current object but over an empty graph

note that we return a pointer as it enables subclasses to return pointers to their types, not Triangulation pointers. See item 25 of the more effective C++.

Implements gum::Triangulation.

Implemented in gum::PartialOrderedTriangulation, gum::OrderedTriangulation, gum::DefaultTriangulation, and gum::UnconstrainedTriangulation.

operator=()

StaticTriangulation& gum::StaticTriangulation::operator= ( const StaticTriangulation &  )

private

forbid copy operator

originalGraph()

const UndiGraph* gum::StaticTriangulation::originalGraph

(

)

const

returns the graph to be triangulated

Warning

if we have not set yet a graph, then originalGraph () will return a nullptr.

reverseEliminationOrder()

const NodeProperty< NodeId >& gum::StaticTriangulation::reverseEliminationOrder

(

)

returns a table indicating, for each node, at which step it was deleted by the triangulation process

setFillIns()

void gum::StaticTriangulation::setFillIns

(

bool

)

sets/unsets the record of the fill-ins in the standard triangulation procedure

setGraph()

void gum::StaticTriangulation::setGraph ( const UndiGraph *  graph, const NodeProperty< Size > *  domsizes  )

virtual

initialize the triangulation data structures for a new graph

Parameters

graph	the graph to be triangulated, i.e., the nodes of which will be eliminated
domsizes	the domain sizes of the nodes to be eliminated

Warning

Note that we allow domsizes to be defined over nodes/variables that do not belong to graph. These sizes will simply be ignored. However, it is compulsory that all the nodes of graph belong to dom_sizes

the graph is not copied but only referenced by the elimination sequence algorithm.

Implements gum::Triangulation.

Reimplemented in gum::PartialOrderedTriangulation, and gum::OrderedTriangulation.

Definition at line 505 of file staticTriangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                                                                 {
    // remove the old graph
    clear();

    if (graph != nullptr) {
      // prepare the size of the data for the new graph
      _elim_order_.resize(graph->size());
      _reverse_elim_order_.resize(graph->size());
      _elim_cliques_.resize(graph->size());
      _added_fill_ins_.resize(graph->size());
      _node_2_max_prime_clique_.resize(graph->size());
    }

    // keep track of the variables passed in argument
    _original_graph_ = graph;
    domain_sizes_    = domsizes;

    // indicate that no triangulation was performed for this graph
    _has_triangulation_           = false;
    _has_triangulated_graph_      = false;
    _has_elimination_tree_        = false;
    _has_junction_tree_           = false;
    _has_max_prime_junction_tree_ = false;
    _has_fill_ins_                = false;
  }

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setMinimalRequirement()

void gum::StaticTriangulation::setMinimalRequirement

(

bool

)

sets/unset the minimality requirement

triangulatedGraph()

const UndiGraph & gum::StaticTriangulation::triangulatedGraph ( )

virtual

returns the triangulated graph

Implements gum::Triangulation.

Definition at line 466 of file staticTriangulation.cpp.

References gum::Set< Key, Alloc >::emplace().

                                                          {
    if (!_has_triangulation_) _triangulate_();

    // if we did not construct the triangulated graph during the triangulation,
    // that is, we just constructed the junction tree, we shall construct it now
    if (!_has_triangulated_graph_) {
      // just in case, be sure that the junction tree has been constructed
      if (!_has_junction_tree_) junctionTree();

      // copy the original graph
      _triangulated_graph_ = *_original_graph_;

      for (const auto clik_id: *_junction_tree_) {
        // for each clique, add the edges necessary to make it complete
        const NodeSet&        clique = _junction_tree_->clique(clik_id);
        std::vector< NodeId > clique_nodes(clique.size());
        unsigned int          i = 0;

        for (const auto node: clique) {
          clique_nodes[i] = node;
          i += 1;
        }

        for (i = 0; i < clique_nodes.size(); ++i) {
          for (unsigned int j = i + 1; j < clique_nodes.size(); ++j) {
            try {
              _triangulated_graph_.addEdge(clique_nodes[i], clique_nodes[j]);
            } catch (DuplicateElement&) {}
          }
        }
      }

      _has_triangulated_graph_ = true;
    }

    return _triangulated_graph_;
  }

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Member Data Documentation

_added_fill_ins_

std::vector< EdgeSet > gum::StaticTriangulation::_added_fill_ins_

private

a vector containing the set of fill-ins added after each node elimination (used by recursive thinning)

Definition at line 294 of file staticTriangulation.h.

_elim_cliques_

NodeProperty< NodeSet > gum::StaticTriangulation::_elim_cliques_

private

the cliques formed by the elimination of the nodes

Definition at line 252 of file staticTriangulation.h.

_elim_order_

std::vector< NodeId > gum::StaticTriangulation::_elim_order_

private

the order in which nodes are eliminated by the algorithm

Definition at line 246 of file staticTriangulation.h.

_elim_tree_

CliqueGraph gum::StaticTriangulation::_elim_tree_

private

the elimination tree computed by the algorithm

Definition at line 255 of file staticTriangulation.h.

_fill_ins_

EdgeSet gum::StaticTriangulation::_fill_ins_

private

the fill-ins added during the whole triangulation process

Definition at line 243 of file staticTriangulation.h.

_has_elimination_tree_

bool gum::StaticTriangulation::_has_elimination_tree_ {false}

private

a boolean indicating whether the elimination tree has been computed

Definition at line 277 of file staticTriangulation.h.

_has_fill_ins_

bool gum::StaticTriangulation::_has_fill_ins_ {false}

private

indicates whether we actually computed fill-ins

Definition at line 287 of file staticTriangulation.h.

_has_junction_tree_

bool gum::StaticTriangulation::_has_junction_tree_ {false}

private

a boolean indicating whether the junction tree has been constructed

Definition at line 280 of file staticTriangulation.h.

_has_max_prime_junction_tree_

bool gum::StaticTriangulation::_has_max_prime_junction_tree_ {false}

private

indicates whether a maximal prime subgraph junction tree has been constructed

Definition at line 284 of file staticTriangulation.h.

_has_triangulated_graph_

bool gum::StaticTriangulation::_has_triangulated_graph_ {false}

private

a boolean indicating whether we have constructed the triangulated graph

Definition at line 274 of file staticTriangulation.h.

_has_triangulation_

bool gum::StaticTriangulation::_has_triangulation_ {false}

private

a boolean indicating whether we have parformed a triangulation

Definition at line 271 of file staticTriangulation.h.

_junction_tree_

const CliqueGraph* gum::StaticTriangulation::_junction_tree_ {nullptr}

private

the junction tree computed by the algorithm

note that the junction tree is owned by the junctionTreeStrategy and, therefore, its deletion from memory is not handled by the static triangulation class.

Definition at line 261 of file staticTriangulation.h.

_max_prime_junction_tree_

CliqueGraph gum::StaticTriangulation::_max_prime_junction_tree_

private

the maximal prime subgraph junction tree computed from the junction tree

Definition at line 264 of file staticTriangulation.h.

_minimality_required_

bool gum::StaticTriangulation::_minimality_required_ {false}

private

indicates whether the triangulation must be minimal

Definition at line 290 of file staticTriangulation.h.

_node_2_max_prime_clique_

NodeProperty< NodeId > gum::StaticTriangulation::_node_2_max_prime_clique_

private

indicates which clique of the max prime junction tree was created by the elmination of a given node (the key of the table)

Definition at line 268 of file staticTriangulation.h.

_original_graph_

const UndiGraph* gum::StaticTriangulation::_original_graph_ {nullptr}

private

a pointer to the (external) original graph (which will be triangulated)

Definition at line 237 of file staticTriangulation.h.

_reverse_elim_order_

NodeProperty< NodeId > gum::StaticTriangulation::_reverse_elim_order_

private

the elimination order (access by NodeId)

Definition at line 249 of file staticTriangulation.h.

_triangulated_graph_

UndiGraph gum::StaticTriangulation::_triangulated_graph_

private

the triangulated graph

Definition at line 240 of file staticTriangulation.h.

_we_want_fill_ins_

bool gum::StaticTriangulation::_we_want_fill_ins_ {false}

private

a boolean indicating if we want fill-ins list with the standard triangulation method

Definition at line 298 of file staticTriangulation.h.

domain_sizes_

const NodeProperty< Size >* gum::Triangulation::domain_sizes_ {nullptr}

protectedinherited

the domain sizes of the variables/nodes of the graph

Definition at line 150 of file triangulation.h.

elimination_sequence_strategy_

EliminationSequenceStrategy* gum::StaticTriangulation::elimination_sequence_strategy_ {nullptr}

protected

the elimination sequence strategy used by the triangulation

Definition at line 229 of file staticTriangulation.h.

junction_tree_strategy_

JunctionTreeStrategy* gum::StaticTriangulation::junction_tree_strategy_ {nullptr}

protected

the junction tree strategy used by the triangulation

Definition at line 232 of file staticTriangulation.h.

---

The documentation for this class was generated from the following files:

• agrum/tools/graphs/algorithms/triangulations/staticTriangulation.h
• agrum/tools/graphs/algorithms/triangulations/staticTriangulation.cpp