separation_tpl.h

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 *       - Pierre-Henri WUILLEMIN(_at_LIP6)                                 *
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#pragma once
 
#include <agrum/base/graphs/algorithms/generic/separation.h>
 
namespace gum::graph {
 
  template < GUM_DiGraphable G >
  bool dSeparated(const G& g, NodeId X, NodeId Y, const NodeSet& Z) {
    NodeSet qX;
    qX.insert(X);
    return !graph::dConnected(g, qX, Z).exists(Y);
  }
 
  template < GUM_DiGraphable G >
  bool dSeparated(const G& g, const NodeSet& X, const NodeSet& Y, const NodeSet& Z) {
    if (!(X * Y).empty()) GUM_ERROR(InvalidArgument, "NodeSets X and Y must be disjoint.")
    return (graph::dConnected(g, X, Z) * Y).empty();
  }
 
  template < GUM_MixedGraphable G >
  bool cSeparated(const G& g, NodeId X, NodeId Y, const NodeSet& Z) {
    NodeSet query{Z};
    query.insert(X);
    query.insert(Y);
    auto moral = moralizedAncestralGraph(g, query);
    for (const auto node: Z)
      if (moral.existsNode(node)) moral.eraseNode(node);
    return !moral.hasUndirectedPath(X, Y);
  }
 
  template < GUM_MixedGraphable G >
  bool cSeparated(const G& g, const NodeSet& X, const NodeSet& Y, const NodeSet& Z) {
    if (!(X * Y).empty()) GUM_ERROR(InvalidArgument, "NodeSets X and Y must be disjoint.")
 
    NodeSet query{Z};
    query += X;
    query += Y;
    auto moral = moralizedAncestralGraph(g, query);
    for (const auto node: Z)
      if (moral.existsNode(node)) moral.eraseNode(node);
 
    const auto cc = moral.chainComponents();
 
    NodeSet Xcc, Ycc;
    for (const auto node: X)
      if (moral.existsNode(node)) Xcc.insert(cc[node]);
    for (const auto node: Y)
      if (moral.existsNode(node)) Ycc.insert(cc[node]);
 
    return (Xcc * Ycc).empty();
  }
 
}   // namespace gum::graph