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rbtree: Add support for augmented rbtrees

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Add support for augmented rbtrees in core rbtree code.

This will be used in subsequent patches, in x86 PAT code, which needs
interval trees to efficiently keep track of PAT ranges.

Signed-off-by: Venkatesh Pallipadi <[email protected]>
LKML-Reference: <[email protected]>
Signed-off-by: Suresh Siddha <[email protected]>
Signed-off-by: H. Peter Anvin <[email protected]>
This commit is contained in:
Pallipadi, Venkatesh 2010-02-10 15:23:44 -08:00 • committed by H. Peter Anvin
commit 17d9ddc72f
3 changed files with 106 additions and 5 deletions
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58
Documentation/rbtree.txt
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@ -190,3 +190,61 @@ Example:
for (node = rb_first(&mytree); node; node = rb_next(node))
printk("key=%s\n", rb_entry(node, struct mytype, node)->keystring);
Support for Augmented rbtrees
-----------------------------
Augmented rbtree is an rbtree with "some" additional data stored in each node.
This data can be used to augment some new functionality to rbtree.
Augmented rbtree is an optional feature built on top of basic rbtree
infrastructure. rbtree user who wants this feature will have an augment
callback function in rb_root initialized.
This callback function will be called from rbtree core routines whenever
a node has a change in one or both of its children. It is the responsibility
of the callback function to recalculate the additional data that is in the
rb node using new children information. Note that if this new additional
data affects the parent node's additional data, then callback function has
to handle it and do the recursive updates.
Interval tree is an example of augmented rb tree. Reference -
"Introduction to Algorithms" by Cormen, Leiserson, Rivest and Stein.
More details about interval trees:
Classical rbtree has a single key and it cannot be directly used to store
interval ranges like [lo:hi] and do a quick lookup for any overlap with a new
lo:hi or to find whether there is an exact match for a new lo:hi.
However, rbtree can be augmented to store such interval ranges in a structured
way making it possible to do efficient lookup and exact match.
This "extra information" stored in each node is the maximum hi
(max_hi) value among all the nodes that are its descendents. This
information can be maintained at each node just be looking at the node
and its immediate children. And this will be used in O(log n) lookup
for lowest match (lowest start address among all possible matches)
with something like:
find_lowest_match(lo, hi, node)
{
lowest_match = NULL;
while (node) {
if (max_hi(node->left) > lo) {
// Lowest overlap if any must be on left side
node = node->left;
} else if (overlap(lo, hi, node)) {
lowest_match = node;
break;
} else if (lo > node->lo) {
// Lowest overlap if any must be on right side
node = node->right;
} else {
break;
}
}
return lowest_match;
}
Finding exact match will be to first find lowest match and then to follow
successor nodes looking for exact match, until the start of a node is beyond
the hi value we are looking for.