// requires: opTypeToIsolate must be LOJ, IJ, or Union
// effects: Given a tree rooted at rootNode, determines if there
// are any FOJs that can be replaced by opTypeToIsolate. If so,
// does that and a returns a new tree with the replaced operators
// Note: Method may modify rootNode's contents and children
internal CellTreeNode IsolateByOperator(CellTreeNode rootNode, CellTreeOpType opTypeToIsolate)
{
Debug.Assert(
opTypeToIsolate == CellTreeOpType.IJ || opTypeToIsolate == CellTreeOpType.LOJ
|| opTypeToIsolate == CellTreeOpType.Union,
"IsolateJoins can only be called for IJs, LOJs, and Unions");
var children = rootNode.Children;
if (children.Count <= 1)
{
// No child or one child - do nothing
return rootNode;
}
// Replace the FOJs with IJs/LOJs/Unions in the children's subtrees first
for (var i = 0; i < children.Count; i++)
{
// Method modifies input as well
children[i] = IsolateByOperator(children[i], opTypeToIsolate);
}
// Only FOJs and LOJs can be coverted (to IJs, Unions, LOJs) --
// so if the node is not that, we can ignore it (or if the node is already of
// the same type that we want)
if (rootNode.OpType != CellTreeOpType.FOJ && rootNode.OpType != CellTreeOpType.LOJ
||
rootNode.OpType == opTypeToIsolate)
{
return rootNode;
}
// Create a new node with the same type as the input cell node type
var newRootNode = new OpCellTreeNode(m_viewgenContext, rootNode.OpType);
// We start a new "group" with one of the children X - we create
// a newChildNode with type "opTypeToIsolate". Then we
// determine if any of the remaining children should be in the
// same group as X.
// childrenSet keeps track of the children that need to be procesed/partitioned
var childrenSet = new ModifiableIteratorCollection<CellTreeNode>(children);
// Find groups with same or subsumed constants and create a join
// or union node for them. We do this so that some of the FOJs
// can be replaced by union and join nodes
//
while (false == childrenSet.IsEmpty)
{
// Start a new "group" with some child node (for the opTypeToIsolate node type)
var groupNode = new OpCellTreeNode(m_viewgenContext, opTypeToIsolate);
var someChild = childrenSet.RemoveOneElement();
groupNode.Add(someChild);
// Go through the remaining children and determine if their
// constants are subsets/equal/disjoint w.r.t the joinNode
// constants.
foreach (var child in childrenSet.Elements())
{
// Check if we can add the child as part of this
// groupNode (with opTypeToIsolate being LOJ, IJ, or Union)
if (TryAddChildToGroup(opTypeToIsolate, child, groupNode))
{
childrenSet.RemoveCurrentOfIterator();
// For LOJ, suppose that child A did not subsume B or
// vice-versa. But child C subsumes both. To ensure
// that we can get A, B, C in the same group, we
// reset the iterator so that when C is added in B's
// loop, we can reconsider A.
//
// For IJ, adding a child to groupNode does not change the range of it,
// so there is no need to reconsider previously skipped children.
//
// For Union, adding a child to groupNode increases the range of the groupNode,
// hence previously skipped (because they weren't disjoint with groupNode) children will continue
// being ignored because they would still have an overlap with one of the nodes inside groupNode.
if (opTypeToIsolate == CellTreeOpType.LOJ)
{
childrenSet.ResetIterator();
}
}
}
// The new Union/LOJ/IJ node needs to be connected to the root
newRootNode.Add(groupNode);
}
return newRootNode.Flatten();
}
// requires: cellTreeNode has a tree such that all its intermediate nodes
// are FOJ nodes only
// effects: Converts the tree rooted at rootNode (recursively) in
// following way and returns a new rootNode -- it partitions
// rootNode's children such that no two different partitions have
// any overlapping constants. These partitions are connected by Union
// nodes (since there is no overlapping).
// Note: Method may modify rootNode's contents and children
private CellTreeNode IsolateUnions(CellTreeNode rootNode)
{
if (rootNode.Children.Count <= 1)
{
// No partitioning of children needs to be done
return(rootNode);
}
Debug.Assert(rootNode.OpType == CellTreeOpType.FOJ, "So far, we have FOJs only");
// Recursively, transform the subtrees rooted at cellTreeNode's children
for (var i = 0; i < rootNode.Children.Count; i++)
{
// Method modifies input as well
rootNode.Children[i] = IsolateUnions(rootNode.Children[i]);
}
// Different children groups are connected by a Union
// node -- the secltion domain of one group is disjoint from
// another group's selection domain, i.e., group A1 contributes
// tuples to the extent which are disjoint from the tuples by
// A2. So we can connect these groups by union alls.
// Inside each group, we continue to connect children of the same
// group using FOJ
var unionNode = new OpCellTreeNode(m_viewgenContext, CellTreeOpType.Union);
// childrenSet keeps track of the children that need to be procesed/partitioned
var childrenSet = new ModifiableIteratorCollection <CellTreeNode>(rootNode.Children);
while (false == childrenSet.IsEmpty)
{
// Start a new group
// Make an FOJ node to connect children of the same group
var fojNode = new OpCellTreeNode(m_viewgenContext, CellTreeOpType.FOJ);
// Add one of the root's children as a child to the foj node
var someChild = childrenSet.RemoveOneElement();
fojNode.Add(someChild);
// We now want a transitive closure of the overlap between the
// the children node. We keep checking each child with the
// fojNode and add it as a child of fojNode if there is an
// overlap. Note that when a node is added to the fojNode,
// its constants are propagated to the fojNode -- so we do
// get transitive closure in terms of intersection
foreach (var child in childrenSet.Elements())
{
if (!IsDisjoint(fojNode, child))
{
fojNode.Add(child);
childrenSet.RemoveCurrentOfIterator();
// To ensure that we get all overlapping node, we
// need to restart checking all the children
childrenSet.ResetIterator();
}
}
// Now we have a group of children nodes rooted at
// fojNode. Add this fojNode to the union
unionNode.Add(fojNode);
}
// The union node as the root of the view
var result = unionNode.Flatten();
return(result);
}
// requires: cellTreeNode has a tree such that all its intermediate nodes
// are FOJ nodes only
// effects: Converts the tree rooted at rootNode (recursively) in
// following way and returns a new rootNode -- it partitions
// rootNode's children such that no two different partitions have
// any overlapping constants. These partitions are connected by Union
// nodes (since there is no overlapping).
// Note: Method may modify rootNode's contents and children
private CellTreeNode IsolateUnions(CellTreeNode rootNode)
{
if (rootNode.Children.Count <= 1)
{
// No partitioning of children needs to be done
return rootNode;
}
Debug.Assert(rootNode.OpType == CellTreeOpType.FOJ, "So far, we have FOJs only");
// Recursively, transform the subtrees rooted at cellTreeNode's children
for (var i = 0; i < rootNode.Children.Count; i++)
{
// Method modifies input as well
rootNode.Children[i] = IsolateUnions(rootNode.Children[i]);
}
// Different children groups are connected by a Union
// node -- the secltion domain of one group is disjoint from
// another group's selection domain, i.e., group A1 contributes
// tuples to the extent which are disjoint from the tuples by
// A2. So we can connect these groups by union alls.
// Inside each group, we continue to connect children of the same
// group using FOJ
var unionNode = new OpCellTreeNode(m_viewgenContext, CellTreeOpType.Union);
// childrenSet keeps track of the children that need to be procesed/partitioned
var childrenSet = new ModifiableIteratorCollection<CellTreeNode>(rootNode.Children);
while (false == childrenSet.IsEmpty)
{
// Start a new group
// Make an FOJ node to connect children of the same group
var fojNode = new OpCellTreeNode(m_viewgenContext, CellTreeOpType.FOJ);
// Add one of the root's children as a child to the foj node
var someChild = childrenSet.RemoveOneElement();
fojNode.Add(someChild);
// We now want a transitive closure of the overlap between the
// the children node. We keep checking each child with the
// fojNode and add it as a child of fojNode if there is an
// overlap. Note that when a node is added to the fojNode,
// its constants are propagated to the fojNode -- so we do
// get transitive closure in terms of intersection
foreach (var child in childrenSet.Elements())
{
if (!IsDisjoint(fojNode, child))
{
fojNode.Add(child);
childrenSet.RemoveCurrentOfIterator();
// To ensure that we get all overlapping node, we
// need to restart checking all the children
childrenSet.ResetIterator();
}
}
// Now we have a group of children nodes rooted at
// fojNode. Add this fojNode to the union
unionNode.Add(fojNode);
}
// The union node as the root of the view
var result = unionNode.Flatten();
return result;
}
// requires: opTypeToIsolate must be LOJ, IJ, or Union
// effects: Given a tree rooted at rootNode, determines if there
// are any FOJs that can be replaced by opTypeToIsolate. If so,
// does that and a returns a new tree with the replaced operators
// Note: Method may modify rootNode's contents and children
internal CellTreeNode IsolateByOperator(CellTreeNode rootNode, CellTreeOpType opTypeToIsolate)
{
Debug.Assert(
opTypeToIsolate == CellTreeOpType.IJ || opTypeToIsolate == CellTreeOpType.LOJ ||
opTypeToIsolate == CellTreeOpType.Union,
"IsolateJoins can only be called for IJs, LOJs, and Unions");
var children = rootNode.Children;
if (children.Count <= 1)
{
// No child or one child - do nothing
return(rootNode);
}
// Replace the FOJs with IJs/LOJs/Unions in the children's subtrees first
for (var i = 0; i < children.Count; i++)
{
// Method modifies input as well
children[i] = IsolateByOperator(children[i], opTypeToIsolate);
}
// Only FOJs and LOJs can be coverted (to IJs, Unions, LOJs) --
// so if the node is not that, we can ignore it (or if the node is already of
// the same type that we want)
if (rootNode.OpType != CellTreeOpType.FOJ && rootNode.OpType != CellTreeOpType.LOJ
||
rootNode.OpType == opTypeToIsolate)
{
return(rootNode);
}
// Create a new node with the same type as the input cell node type
var newRootNode = new OpCellTreeNode(m_viewgenContext, rootNode.OpType);
// We start a new "group" with one of the children X - we create
// a newChildNode with type "opTypeToIsolate". Then we
// determine if any of the remaining children should be in the
// same group as X.
// childrenSet keeps track of the children that need to be procesed/partitioned
var childrenSet = new ModifiableIteratorCollection <CellTreeNode>(children);
// Find groups with same or subsumed constants and create a join
// or union node for them. We do this so that some of the FOJs
// can be replaced by union and join nodes
//
while (false == childrenSet.IsEmpty)
{
// Start a new "group" with some child node (for the opTypeToIsolate node type)
var groupNode = new OpCellTreeNode(m_viewgenContext, opTypeToIsolate);
var someChild = childrenSet.RemoveOneElement();
groupNode.Add(someChild);
// Go through the remaining children and determine if their
// constants are subsets/equal/disjoint w.r.t the joinNode
// constants.
foreach (var child in childrenSet.Elements())
{
// Check if we can add the child as part of this
// groupNode (with opTypeToIsolate being LOJ, IJ, or Union)
if (TryAddChildToGroup(opTypeToIsolate, child, groupNode))
{
childrenSet.RemoveCurrentOfIterator();
// For LOJ, suppose that child A did not subsume B or
// vice-versa. But child C subsumes both. To ensure
// that we can get A, B, C in the same group, we
// reset the iterator so that when C is added in B's
// loop, we can reconsider A.
//
// For IJ, adding a child to groupNode does not change the range of it,
// so there is no need to reconsider previously skipped children.
//
// For Union, adding a child to groupNode increases the range of the groupNode,
// hence previously skipped (because they weren't disjoint with groupNode) children will continue
// being ignored because they would still have an overlap with one of the nodes inside groupNode.
if (opTypeToIsolate == CellTreeOpType.LOJ)
{
childrenSet.ResetIterator();
}
}
}
// The new Union/LOJ/IJ node needs to be connected to the root
newRootNode.Add(groupNode);
}
return(newRootNode.Flatten());
}