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+//===- Graph.h - PBQP Graph -------------------------------------*- C++ -*-===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+//
+// PBQP Graph class.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_CODEGEN_PBQP_GRAPH_H
+#define LLVM_CODEGEN_PBQP_GRAPH_H
+
+#include "llvm/ADT/STLExtras.h"
+#include <algorithm>
+#include <cassert>
+#include <iterator>
+#include <limits>
+#include <vector>
+
+namespace llvm {
+namespace PBQP {
+
+  class GraphBase {
+  public:
+    using NodeId = unsigned;
+    using EdgeId = unsigned;
+
+    /// @brief Returns a value representing an invalid (non-existent) node.
+    static NodeId invalidNodeId() {
+      return std::numeric_limits<NodeId>::max();
+    }
+
+    /// @brief Returns a value representing an invalid (non-existent) edge.
+    static EdgeId invalidEdgeId() {
+      return std::numeric_limits<EdgeId>::max();
+    }
+  };
+
+  /// PBQP Graph class.
+  /// Instances of this class describe PBQP problems.
+  ///
+  template <typename SolverT>
+  class Graph : public GraphBase {
+  private:
+    using CostAllocator = typename SolverT::CostAllocator;
+
+  public:
+    using RawVector = typename SolverT::RawVector;
+    using RawMatrix = typename SolverT::RawMatrix;
+    using Vector = typename SolverT::Vector;
+    using Matrix = typename SolverT::Matrix;
+    using VectorPtr = typename CostAllocator::VectorPtr;
+    using MatrixPtr = typename CostAllocator::MatrixPtr;
+    using NodeMetadata = typename SolverT::NodeMetadata;
+    using EdgeMetadata = typename SolverT::EdgeMetadata;
+    using GraphMetadata = typename SolverT::GraphMetadata;
+
+  private:
+    class NodeEntry {
+    public:
+      using AdjEdgeList = std::vector<EdgeId>;
+      using AdjEdgeIdx = AdjEdgeList::size_type;
+      using AdjEdgeItr = AdjEdgeList::const_iterator;
+
+      NodeEntry(VectorPtr Costs) : Costs(std::move(Costs)) {}
+
+      static AdjEdgeIdx getInvalidAdjEdgeIdx() {
+        return std::numeric_limits<AdjEdgeIdx>::max();
+      }
+
+      AdjEdgeIdx addAdjEdgeId(EdgeId EId) {
+        AdjEdgeIdx Idx = AdjEdgeIds.size();
+        AdjEdgeIds.push_back(EId);
+        return Idx;
+      }
+
+      void removeAdjEdgeId(Graph &G, NodeId ThisNId, AdjEdgeIdx Idx) {
+        // Swap-and-pop for fast removal.
+        //   1) Update the adj index of the edge currently at back().
+        //   2) Move last Edge down to Idx.
+        //   3) pop_back()
+        // If Idx == size() - 1 then the setAdjEdgeIdx and swap are
+        // redundant, but both operations are cheap.
+        G.getEdge(AdjEdgeIds.back()).setAdjEdgeIdx(ThisNId, Idx);
+        AdjEdgeIds[Idx] = AdjEdgeIds.back();
+        AdjEdgeIds.pop_back();
+      }
+
+      const AdjEdgeList& getAdjEdgeIds() const { return AdjEdgeIds; }
+
+      VectorPtr Costs;
+      NodeMetadata Metadata;
+
+    private:
+      AdjEdgeList AdjEdgeIds;
+    };
+
+    class EdgeEntry {
+    public:
+      EdgeEntry(NodeId N1Id, NodeId N2Id, MatrixPtr Costs)
+          : Costs(std::move(Costs)) {
+        NIds[0] = N1Id;
+        NIds[1] = N2Id;
+        ThisEdgeAdjIdxs[0] = NodeEntry::getInvalidAdjEdgeIdx();
+        ThisEdgeAdjIdxs[1] = NodeEntry::getInvalidAdjEdgeIdx();
+      }
+
+      void connectToN(Graph &G, EdgeId ThisEdgeId, unsigned NIdx) {
+        assert(ThisEdgeAdjIdxs[NIdx] == NodeEntry::getInvalidAdjEdgeIdx() &&
+               "Edge already connected to NIds[NIdx].");
+        NodeEntry &N = G.getNode(NIds[NIdx]);
+        ThisEdgeAdjIdxs[NIdx] = N.addAdjEdgeId(ThisEdgeId);
+      }
+
+      void connect(Graph &G, EdgeId ThisEdgeId) {
+        connectToN(G, ThisEdgeId, 0);
+        connectToN(G, ThisEdgeId, 1);
+      }
+
+      void setAdjEdgeIdx(NodeId NId, typename NodeEntry::AdjEdgeIdx NewIdx) {
+        if (NId == NIds[0])
+          ThisEdgeAdjIdxs[0] = NewIdx;
+        else {
+          assert(NId == NIds[1] && "Edge not connected to NId");
+          ThisEdgeAdjIdxs[1] = NewIdx;
+        }
+      }
+
+      void disconnectFromN(Graph &G, unsigned NIdx) {
+        assert(ThisEdgeAdjIdxs[NIdx] != NodeEntry::getInvalidAdjEdgeIdx() &&
+               "Edge not connected to NIds[NIdx].");
+        NodeEntry &N = G.getNode(NIds[NIdx]);
+        N.removeAdjEdgeId(G, NIds[NIdx], ThisEdgeAdjIdxs[NIdx]);
+        ThisEdgeAdjIdxs[NIdx] = NodeEntry::getInvalidAdjEdgeIdx();
+      }
+
+      void disconnectFrom(Graph &G, NodeId NId) {
+        if (NId == NIds[0])
+          disconnectFromN(G, 0);
+        else {
+          assert(NId == NIds[1] && "Edge does not connect NId");
+          disconnectFromN(G, 1);
+        }
+      }
+
+      NodeId getN1Id() const { return NIds[0]; }
+      NodeId getN2Id() const { return NIds[1]; }
+
+      MatrixPtr Costs;
+      EdgeMetadata Metadata;
+
+    private:
+      NodeId NIds[2];
+      typename NodeEntry::AdjEdgeIdx ThisEdgeAdjIdxs[2];
+    };
+
+    // ----- MEMBERS -----
+
+    GraphMetadata Metadata;
+    CostAllocator CostAlloc;
+    SolverT *Solver = nullptr;
+
+    using NodeVector = std::vector<NodeEntry>;
+    using FreeNodeVector = std::vector<NodeId>;
+    NodeVector Nodes;
+    FreeNodeVector FreeNodeIds;
+
+    using EdgeVector = std::vector<EdgeEntry>;
+    using FreeEdgeVector = std::vector<EdgeId>;
+    EdgeVector Edges;
+    FreeEdgeVector FreeEdgeIds;
+
+    Graph(const Graph &Other) {}
+
+    // ----- INTERNAL METHODS -----
+
+    NodeEntry &getNode(NodeId NId) {
+      assert(NId < Nodes.size() && "Out of bound NodeId");
+      return Nodes[NId];
+    }
+    const NodeEntry &getNode(NodeId NId) const {
+      assert(NId < Nodes.size() && "Out of bound NodeId");
+      return Nodes[NId];
+    }
+
+    EdgeEntry& getEdge(EdgeId EId) { return Edges[EId]; }
+    const EdgeEntry& getEdge(EdgeId EId) const { return Edges[EId]; }
+
+    NodeId addConstructedNode(NodeEntry N) {
+      NodeId NId = 0;
+      if (!FreeNodeIds.empty()) {
+        NId = FreeNodeIds.back();
+        FreeNodeIds.pop_back();
+        Nodes[NId] = std::move(N);
+      } else {
+        NId = Nodes.size();
+        Nodes.push_back(std::move(N));
+      }
+      return NId;
+    }
+
+    EdgeId addConstructedEdge(EdgeEntry E) {
+      assert(findEdge(E.getN1Id(), E.getN2Id()) == invalidEdgeId() &&
+             "Attempt to add duplicate edge.");
+      EdgeId EId = 0;
+      if (!FreeEdgeIds.empty()) {
+        EId = FreeEdgeIds.back();
+        FreeEdgeIds.pop_back();
+        Edges[EId] = std::move(E);
+      } else {
+        EId = Edges.size();
+        Edges.push_back(std::move(E));
+      }
+
+      EdgeEntry &NE = getEdge(EId);
+
+      // Add the edge to the adjacency sets of its nodes.
+      NE.connect(*this, EId);
+      return EId;
+    }
+
+    void operator=(const Graph &Other) {}
+
+  public:
+    using AdjEdgeItr = typename NodeEntry::AdjEdgeItr;
+
+    class NodeItr {
+    public:
+      using iterator_category = std::forward_iterator_tag;
+      using value_type = NodeId;
+      using difference_type = int;
+      using pointer = NodeId *;
+      using reference = NodeId &;
+
+      NodeItr(NodeId CurNId, const Graph &G)
+        : CurNId(CurNId), EndNId(G.Nodes.size()), FreeNodeIds(G.FreeNodeIds) {
+        this->CurNId = findNextInUse(CurNId); // Move to first in-use node id
+      }
+
+      bool operator==(const NodeItr &O) const { return CurNId == O.CurNId; }
+      bool operator!=(const NodeItr &O) const { return !(*this == O); }
+      NodeItr& operator++() { CurNId = findNextInUse(++CurNId); return *this; }
+      NodeId operator*() const { return CurNId; }
+
+    private:
+      NodeId findNextInUse(NodeId NId) const {
+        while (NId < EndNId && is_contained(FreeNodeIds, NId)) {
+          ++NId;
+        }
+        return NId;
+      }
+
+      NodeId CurNId, EndNId;
+      const FreeNodeVector &FreeNodeIds;
+    };
+
+    class EdgeItr {
+    public:
+      EdgeItr(EdgeId CurEId, const Graph &G)
+        : CurEId(CurEId), EndEId(G.Edges.size()), FreeEdgeIds(G.FreeEdgeIds) {
+        this->CurEId = findNextInUse(CurEId); // Move to first in-use edge id
+      }
+
+      bool operator==(const EdgeItr &O) const { return CurEId == O.CurEId; }
+      bool operator!=(const EdgeItr &O) const { return !(*this == O); }
+      EdgeItr& operator++() { CurEId = findNextInUse(++CurEId); return *this; }
+      EdgeId operator*() const { return CurEId; }
+
+    private:
+      EdgeId findNextInUse(EdgeId EId) const {
+        while (EId < EndEId && is_contained(FreeEdgeIds, EId)) {
+          ++EId;
+        }
+        return EId;
+      }
+
+      EdgeId CurEId, EndEId;
+      const FreeEdgeVector &FreeEdgeIds;
+    };
+
+    class NodeIdSet {
+    public:
+      NodeIdSet(const Graph &G) : G(G) {}
+
+      NodeItr begin() const { return NodeItr(0, G); }
+      NodeItr end() const { return NodeItr(G.Nodes.size(), G); }
+
+      bool empty() const { return G.Nodes.empty(); }
+
+      typename NodeVector::size_type size() const {
+        return G.Nodes.size() - G.FreeNodeIds.size();
+      }
+
+    private:
+      const Graph& G;
+    };
+
+    class EdgeIdSet {
+    public:
+      EdgeIdSet(const Graph &G) : G(G) {}
+
+      EdgeItr begin() const { return EdgeItr(0, G); }
+      EdgeItr end() const { return EdgeItr(G.Edges.size(), G); }
+
+      bool empty() const { return G.Edges.empty(); }
+
+      typename NodeVector::size_type size() const {
+        return G.Edges.size() - G.FreeEdgeIds.size();
+      }
+
+    private:
+      const Graph& G;
+    };
+
+    class AdjEdgeIdSet {
+    public:
+      AdjEdgeIdSet(const NodeEntry &NE) : NE(NE) {}
+
+      typename NodeEntry::AdjEdgeItr begin() const {
+        return NE.getAdjEdgeIds().begin();
+      }
+
+      typename NodeEntry::AdjEdgeItr end() const {
+        return NE.getAdjEdgeIds().end();
+      }
+
+      bool empty() const { return NE.getAdjEdgeIds().empty(); }
+
+      typename NodeEntry::AdjEdgeList::size_type size() const {
+        return NE.getAdjEdgeIds().size();
+      }
+
+    private:
+      const NodeEntry &NE;
+    };
+
+    /// @brief Construct an empty PBQP graph.
+    Graph() = default;
+
+    /// @brief Construct an empty PBQP graph with the given graph metadata.
+    Graph(GraphMetadata Metadata) : Metadata(std::move(Metadata)) {}
+
+    /// @brief Get a reference to the graph metadata.
+    GraphMetadata& getMetadata() { return Metadata; }
+
+    /// @brief Get a const-reference to the graph metadata.
+    const GraphMetadata& getMetadata() const { return Metadata; }
+
+    /// @brief Lock this graph to the given solver instance in preparation
+    /// for running the solver. This method will call solver.handleAddNode for
+    /// each node in the graph, and handleAddEdge for each edge, to give the
+    /// solver an opportunity to set up any requried metadata.
+    void setSolver(SolverT &S) {
+      assert(!Solver && "Solver already set. Call unsetSolver().");
+      Solver = &S;
+      for (auto NId : nodeIds())
+        Solver->handleAddNode(NId);
+      for (auto EId : edgeIds())
+        Solver->handleAddEdge(EId);
+    }
+
+    /// @brief Release from solver instance.
+    void unsetSolver() {
+      assert(Solver && "Solver not set.");
+      Solver = nullptr;
+    }
+
+    /// @brief Add a node with the given costs.
+    /// @param Costs Cost vector for the new node.
+    /// @return Node iterator for the added node.
+    template <typename OtherVectorT>
+    NodeId addNode(OtherVectorT Costs) {
+      // Get cost vector from the problem domain
+      VectorPtr AllocatedCosts = CostAlloc.getVector(std::move(Costs));
+      NodeId NId = addConstructedNode(NodeEntry(AllocatedCosts));
+      if (Solver)
+        Solver->handleAddNode(NId);
+      return NId;
+    }
+
+    /// @brief Add a node bypassing the cost allocator.
+    /// @param Costs Cost vector ptr for the new node (must be convertible to
+    ///        VectorPtr).
+    /// @return Node iterator for the added node.
+    ///
+    ///   This method allows for fast addition of a node whose costs don't need
+    /// to be passed through the cost allocator. The most common use case for
+    /// this is when duplicating costs from an existing node (when using a
+    /// pooling allocator). These have already been uniqued, so we can avoid
+    /// re-constructing and re-uniquing them by attaching them directly to the
+    /// new node.
+    template <typename OtherVectorPtrT>
+    NodeId addNodeBypassingCostAllocator(OtherVectorPtrT Costs) {
+      NodeId NId = addConstructedNode(NodeEntry(Costs));
+      if (Solver)
+        Solver->handleAddNode(NId);
+      return NId;
+    }
+
+    /// @brief Add an edge between the given nodes with the given costs.
+    /// @param N1Id First node.
+    /// @param N2Id Second node.
+    /// @param Costs Cost matrix for new edge.
+    /// @return Edge iterator for the added edge.
+    template <typename OtherVectorT>
+    EdgeId addEdge(NodeId N1Id, NodeId N2Id, OtherVectorT Costs) {
+      assert(getNodeCosts(N1Id).getLength() == Costs.getRows() &&
+             getNodeCosts(N2Id).getLength() == Costs.getCols() &&
+             "Matrix dimensions mismatch.");
+      // Get cost matrix from the problem domain.
+      MatrixPtr AllocatedCosts = CostAlloc.getMatrix(std::move(Costs));
+      EdgeId EId = addConstructedEdge(EdgeEntry(N1Id, N2Id, AllocatedCosts));
+      if (Solver)
+        Solver->handleAddEdge(EId);
+      return EId;
+    }
+
+    /// @brief Add an edge bypassing the cost allocator.
+    /// @param N1Id First node.
+    /// @param N2Id Second node.
+    /// @param Costs Cost matrix for new edge.
+    /// @return Edge iterator for the added edge.
+    ///
+    ///   This method allows for fast addition of an edge whose costs don't need
+    /// to be passed through the cost allocator. The most common use case for
+    /// this is when duplicating costs from an existing edge (when using a
+    /// pooling allocator). These have already been uniqued, so we can avoid
+    /// re-constructing and re-uniquing them by attaching them directly to the
+    /// new edge.
+    template <typename OtherMatrixPtrT>
+    NodeId addEdgeBypassingCostAllocator(NodeId N1Id, NodeId N2Id,
+                                         OtherMatrixPtrT Costs) {
+      assert(getNodeCosts(N1Id).getLength() == Costs->getRows() &&
+             getNodeCosts(N2Id).getLength() == Costs->getCols() &&
+             "Matrix dimensions mismatch.");
+      // Get cost matrix from the problem domain.
+      EdgeId EId = addConstructedEdge(EdgeEntry(N1Id, N2Id, Costs));
+      if (Solver)
+        Solver->handleAddEdge(EId);
+      return EId;
+    }
+
+    /// @brief Returns true if the graph is empty.
+    bool empty() const { return NodeIdSet(*this).empty(); }
+
+    NodeIdSet nodeIds() const { return NodeIdSet(*this); }
+    EdgeIdSet edgeIds() const { return EdgeIdSet(*this); }
+
+    AdjEdgeIdSet adjEdgeIds(NodeId NId) { return AdjEdgeIdSet(getNode(NId)); }
+
+    /// @brief Get the number of nodes in the graph.
+    /// @return Number of nodes in the graph.
+    unsigned getNumNodes() const { return NodeIdSet(*this).size(); }
+
+    /// @brief Get the number of edges in the graph.
+    /// @return Number of edges in the graph.
+    unsigned getNumEdges() const { return EdgeIdSet(*this).size(); }
+
+    /// @brief Set a node's cost vector.
+    /// @param NId Node to update.
+    /// @param Costs New costs to set.
+    template <typename OtherVectorT>
+    void setNodeCosts(NodeId NId, OtherVectorT Costs) {
+      VectorPtr AllocatedCosts = CostAlloc.getVector(std::move(Costs));
+      if (Solver)
+        Solver->handleSetNodeCosts(NId, *AllocatedCosts);
+      getNode(NId).Costs = AllocatedCosts;
+    }
+
+    /// @brief Get a VectorPtr to a node's cost vector. Rarely useful - use
+    ///        getNodeCosts where possible.
+    /// @param NId Node id.
+    /// @return VectorPtr to node cost vector.
+    ///
+    ///   This method is primarily useful for duplicating costs quickly by
+    /// bypassing the cost allocator. See addNodeBypassingCostAllocator. Prefer
+    /// getNodeCosts when dealing with node cost values.
+    const VectorPtr& getNodeCostsPtr(NodeId NId) const {
+      return getNode(NId).Costs;
+    }
+
+    /// @brief Get a node's cost vector.
+    /// @param NId Node id.
+    /// @return Node cost vector.
+    const Vector& getNodeCosts(NodeId NId) const {
+      return *getNodeCostsPtr(NId);
+    }
+
+    NodeMetadata& getNodeMetadata(NodeId NId) {
+      return getNode(NId).Metadata;
+    }
+
+    const NodeMetadata& getNodeMetadata(NodeId NId) const {
+      return getNode(NId).Metadata;
+    }
+
+    typename NodeEntry::AdjEdgeList::size_type getNodeDegree(NodeId NId) const {
+      return getNode(NId).getAdjEdgeIds().size();
+    }
+
+    /// @brief Update an edge's cost matrix.
+    /// @param EId Edge id.
+    /// @param Costs New cost matrix.
+    template <typename OtherMatrixT>
+    void updateEdgeCosts(EdgeId EId, OtherMatrixT Costs) {
+      MatrixPtr AllocatedCosts = CostAlloc.getMatrix(std::move(Costs));
+      if (Solver)
+        Solver->handleUpdateCosts(EId, *AllocatedCosts);
+      getEdge(EId).Costs = AllocatedCosts;
+    }
+
+    /// @brief Get a MatrixPtr to a node's cost matrix. Rarely useful - use
+    ///        getEdgeCosts where possible.
+    /// @param EId Edge id.
+    /// @return MatrixPtr to edge cost matrix.
+    ///
+    ///   This method is primarily useful for duplicating costs quickly by
+    /// bypassing the cost allocator. See addNodeBypassingCostAllocator. Prefer
+    /// getEdgeCosts when dealing with edge cost values.
+    const MatrixPtr& getEdgeCostsPtr(EdgeId EId) const {
+      return getEdge(EId).Costs;
+    }
+
+    /// @brief Get an edge's cost matrix.
+    /// @param EId Edge id.
+    /// @return Edge cost matrix.
+    const Matrix& getEdgeCosts(EdgeId EId) const {
+      return *getEdge(EId).Costs;
+    }
+
+    EdgeMetadata& getEdgeMetadata(EdgeId EId) {
+      return getEdge(EId).Metadata;
+    }
+
+    const EdgeMetadata& getEdgeMetadata(EdgeId EId) const {
+      return getEdge(EId).Metadata;
+    }
+
+    /// @brief Get the first node connected to this edge.
+    /// @param EId Edge id.
+    /// @return The first node connected to the given edge.
+    NodeId getEdgeNode1Id(EdgeId EId) const {
+      return getEdge(EId).getN1Id();
+    }
+
+    /// @brief Get the second node connected to this edge.
+    /// @param EId Edge id.
+    /// @return The second node connected to the given edge.
+    NodeId getEdgeNode2Id(EdgeId EId) const {
+      return getEdge(EId).getN2Id();
+    }
+
+    /// @brief Get the "other" node connected to this edge.
+    /// @param EId Edge id.
+    /// @param NId Node id for the "given" node.
+    /// @return The iterator for the "other" node connected to this edge.
+    NodeId getEdgeOtherNodeId(EdgeId EId, NodeId NId) {
+      EdgeEntry &E = getEdge(EId);
+      if (E.getN1Id() == NId) {
+        return E.getN2Id();
+      } // else
+      return E.getN1Id();
+    }
+
+    /// @brief Get the edge connecting two nodes.
+    /// @param N1Id First node id.
+    /// @param N2Id Second node id.
+    /// @return An id for edge (N1Id, N2Id) if such an edge exists,
+    ///         otherwise returns an invalid edge id.
+    EdgeId findEdge(NodeId N1Id, NodeId N2Id) {
+      for (auto AEId : adjEdgeIds(N1Id)) {
+        if ((getEdgeNode1Id(AEId) == N2Id) ||
+            (getEdgeNode2Id(AEId) == N2Id)) {
+          return AEId;
+        }
+      }
+      return invalidEdgeId();
+    }
+
+    /// @brief Remove a node from the graph.
+    /// @param NId Node id.
+    void removeNode(NodeId NId) {
+      if (Solver)
+        Solver->handleRemoveNode(NId);
+      NodeEntry &N = getNode(NId);
+      // TODO: Can this be for-each'd?
+      for (AdjEdgeItr AEItr = N.adjEdgesBegin(),
+             AEEnd = N.adjEdgesEnd();
+           AEItr != AEEnd;) {
+        EdgeId EId = *AEItr;
+        ++AEItr;
+        removeEdge(EId);
+      }
+      FreeNodeIds.push_back(NId);
+    }
+
+    /// @brief Disconnect an edge from the given node.
+    ///
+    /// Removes the given edge from the adjacency list of the given node.
+    /// This operation leaves the edge in an 'asymmetric' state: It will no
+    /// longer appear in an iteration over the given node's (NId's) edges, but
+    /// will appear in an iteration over the 'other', unnamed node's edges.
+    ///
+    /// This does not correspond to any normal graph operation, but exists to
+    /// support efficient PBQP graph-reduction based solvers. It is used to
+    /// 'effectively' remove the unnamed node from the graph while the solver
+    /// is performing the reduction. The solver will later call reconnectNode
+    /// to restore the edge in the named node's adjacency list.
+    ///
+    /// Since the degree of a node is the number of connected edges,
+    /// disconnecting an edge from a node 'u' will cause the degree of 'u' to
+    /// drop by 1.
+    ///
+    /// A disconnected edge WILL still appear in an iteration over the graph
+    /// edges.
+    ///
+    /// A disconnected edge should not be removed from the graph, it should be
+    /// reconnected first.
+    ///
+    /// A disconnected edge can be reconnected by calling the reconnectEdge
+    /// method.
+    void disconnectEdge(EdgeId EId, NodeId NId) {
+      if (Solver)
+        Solver->handleDisconnectEdge(EId, NId);
+
+      EdgeEntry &E = getEdge(EId);
+      E.disconnectFrom(*this, NId);
+    }
+
+    /// @brief Convenience method to disconnect all neighbours from the given
+    ///        node.
+    void disconnectAllNeighborsFromNode(NodeId NId) {
+      for (auto AEId : adjEdgeIds(NId))
+        disconnectEdge(AEId, getEdgeOtherNodeId(AEId, NId));
+    }
+
+    /// @brief Re-attach an edge to its nodes.
+    ///
+    /// Adds an edge that had been previously disconnected back into the
+    /// adjacency set of the nodes that the edge connects.
+    void reconnectEdge(EdgeId EId, NodeId NId) {
+      EdgeEntry &E = getEdge(EId);
+      E.connectTo(*this, EId, NId);
+      if (Solver)
+        Solver->handleReconnectEdge(EId, NId);
+    }
+
+    /// @brief Remove an edge from the graph.
+    /// @param EId Edge id.
+    void removeEdge(EdgeId EId) {
+      if (Solver)
+        Solver->handleRemoveEdge(EId);
+      EdgeEntry &E = getEdge(EId);
+      E.disconnect();
+      FreeEdgeIds.push_back(EId);
+      Edges[EId].invalidate();
+    }
+
+    /// @brief Remove all nodes and edges from the graph.
+    void clear() {
+      Nodes.clear();
+      FreeNodeIds.clear();
+      Edges.clear();
+      FreeEdgeIds.clear();
+    }
+  };
+
+} // end namespace PBQP
+} // end namespace llvm
+
+#endif // LLVM_CODEGEN_PBQP_GRAPH_HPP