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Diffstat (limited to 'Documentation/rbtree.txt')

-rw-r--r-- | Documentation/rbtree.txt | 58 |

1 files changed, 58 insertions, 0 deletions

diff --git a/Documentation/rbtree.txt b/Documentation/rbtree.txt index aae8355d3166..221f38be98f4 100644 --- a/Documentation/rbtree.txt +++ b/Documentation/rbtree.txt @@ -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. |