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$Id: red-black,v 1.9 2004/03/05 05:04:46 marka Exp $

Red-Black Tree Implementation Notes

OVERVIEW

BIND9's basic name storage mechanism is to use a modified form of

balanced binary tree known as a red-black tree. Red-black trees

provide for relatively efficient storage, retrieval and removal of

data while maintaining the lexical order of all stored keys, a

necessary function for DNS security.

DESCRIPTION

A red-black tree is a balanced binary tree named for the coloring that

is done in the tree, identifying each node as either red or black.

There are two simple rules for maintaining the color of nodes:

(1) A red node has only black children.

(2) The path from the root to any leaf node always includes the

same number of black nodes.

Whenever a key is added or removed, adjustments are made to adhere to

those two rules. These adjustments are relatively cheap to make but

maintain the balance of the tree, thus making for efficient addition,

lookup and deletion operations, all of which are O(log N). The color

of a node is not relevant to external users of the tree; it is needed

only to maintain the balance of the tree.

For more information on basic red-black trees, see _Introduction to

Algorithms_, Cormen, Leiserson, and Rivest, MIT Press / McGraw Hill,

1990, ISBN 0-262-03141-8, chapter 14.

In BIND9, the red-black tree implementation uses DNS names as keys,

and can store arbitrary data with each key value. "name" and "key"

are used interchangably in this document.

The basic red-black tree algorithm is further adapted for use in BIND9

to incorporate the notion of hierarchy, creating a tree of red-black

trees. Where there is more than one name with a common suffix, all

names with that suffix are stored in their own red-black tree, with a

down pointer from the suffix locating the subtree.

For example, consider storing the following names:

a x.d.e.f o.w.y.d.e.f

b z.d.e.f p.w.y.d.e.f

c g.h q.w.y.d.e.f

No matter which order the keys were added, this would result in a tree

that can be visualized as:

b

/ \

a d.e.f

/|\

c | g.h

|

w.y

/|\

x | z

|

p

/ \

o q

This tree shows that when there is no key for a particular label, and

when there is only one known label for its immediate subordinate, then

multiple labels can appear in a single node, such as at d.e.f and g.h.

It also demonstrates that there can be more nodes in the tree of trees

than there are actual keys (which degrades the O(log N) performance

marginally); the nodes at d.e.f and w.y do not represent keys.

As an aside, remember that when ordering DNS names, labels are

examined from the right, therefore w.y sorts after x and before z.

A split can occur not only on a regular label boundary, but also

between any two bits in an EDNS bitstring label. The common-suffix

rules will be applied to keep as many bits together as possible.

In the current implementation of the tree of trees, a node is

considered to "formally" exist only if it has data associated with

it. So if the above tree then had the key d.e.f added to it, the

operation would succeed rather than getting an "already exists"

error.

Along the same lines, if a key is added with a name which is a proper

superdomain of the name stored in an existing node, the operation will

succeed by splitting the existing node into one node that is the key

and another node that is the remaining parts of the name. Adding e.f

to the above tree results in the top level red-black tree having a

node named e.f where the current d.e.f is, and a down pointer from

d.e.f to a "tree" of a single node named d. The down pointer from d

would be kept to the level which has x, w.y, and z.

A similar split of d.e.f would occur if the name k.e.f were added.

The top level tree would have the node e.f with a down pointer to a

level that had both d and k, and d would continue to have its down

pointer to the x, w.y and z level.

It is guaranteed when splitting that external references to the node

that is split will remain valid --- in the previous examples, anything

that was pointing to the node that was d.e.f will still point to the

node that is now just d.

When deleting keys, nodes can be rejoined. If both of p.w.y.d.e.f and

q.w.y.d.e.f were removed from the example tree, the node named w.y

would become o.w.y. Unlike splitting, it is _not_ guaranteed that

external references remain consistent; sometimes they will, sometimes

they won't. Also, note that deletion is not perfectly symmetric with

addition. If you "undo" the last addition with a deletion of the same

key then the tree of trees is not guaranteed to have exactly the same

structure as it had prior to the addition. Sometimes, but not always.

Rejoining does not happen if it would violate any of the rules that

cause a split. o would not be rejoined with w.y if w.y had data

associated with the key; o would remain as a single node on its own

level. This emphasizes the rule that a node is considered to formally

exist only if data is associated with it, because even if w.y.d.e.f

had been explicitly added as a key but with no data, then o would

still be merged with the w.y node when p and q were deleted.

Searching for a node generally returns one of three possible results:

either the key is found, a superdomain (partial match) of the key is

found, or no part of the key is found. The first and last are rather

obvious, and the second result basically means that a hierarchically

enclosing name is found; e.g, searching for bb.rc.vix.com turned up

rc.vix.com, but not the full name.

No locking is done within the RBT library. @@@

CHAINS

@@@

When a partial match is made, level_matches is set while the chain

points to the partial match node that was found. Then the chain is

adjusted to point to the DNSSEC predecessor node, which might not even

be under the same top level domain as the name that was searched for.

For example, consider a database that had only the names vix.com and

isc.org. A search for uu.net would leave the chain pointed to

vix.com, the DNSSEC predecessor. Though this might first appear to

cause level_matches to be bogus because the chain has been unwound and

sent down another path, note that the partial match node will always

be in the chain of the predecessor, too --- and often the partial

match node will be the predecessor itself. In the vix.com/isc.org

example, the search for uu.net finds a partial match at ".", which is

of course also in the path to the vix.com predecessor. A search for

www.isc.org would find that isc.org is both the partial match and the

predecessor.

EXTERNAL PROGRAMMATIC DETAILS

This section details the functions used to interact with the BIND9

red-black tree library, or RBT for short.

A source file that will be using RBT will usually need to include

<dns/rbt.h>. This header file automatically includes <isc/result.h),

<isc/mem.h>, <dns/types.h>, and <dns/name.h>.

The rbt.h file has more complete descriptions of each of the functions

named here, including what is required for each argument, what each

function ensures (and might not ensure) will occur, and the full range

of possible results for each call. Note well: if a function returns a

dns_result_t rather than void, it definitely means there is something

that can go possibly wrong in the function and it should be checked by

the caller.

A new tree of trees must be initialized using:

dns_result_t dns_rbt_create(isc_mem_t *mctx, void (*deleter)(void *, void *),

void *deleter_arg, dns_rbt_t **rbtp);

The memory context, mctx, must be a non-null pointer that was

initialized with isc_mem_create(). The deleter argument, if non-null,

should point to a function that is responsible for cleaning up any

memory associated with the data pointer of a node when the node is

deleted. It is passed the deleted node's data pointer as its first

argument and deleter_arg as its second argument.

After initializing an RBT manager, to add keys to the tree, use:

dns_result_t dns_rbt_addname(dns_rbt_t *rbt, dns_name_t *name, void *data);

The name _must_ be an absolute name. It is not required that the data

pointer be non-null, but it is recommended that it point to something,

even just invalid memory, because of the various searching and

deletion issues described in the previous section. The RBT code will

not attempt to dereference the pointer.

To find a key in the tree, use:

dns_result_t dns_rbt_findname(dns_rbt_t *rbt, dns_name_t *name, void **data);

The data parameter must not be NULL, but *data must be NULL. The

result will be either DNS_R_SUCCESS, DNS_R_PARTIALMATCH or

DNS_R_NOTFOUND. In the first case, an exact match was found for the

name and there was an associate data pointer, which is returned via

the data parameter. A partial match results when the name has not

been found but a superdomain name, with data, does exist; then the

data for that name is returned in the data parameter. If no data is

found for the name or a superdomain, *data will remain NULL.

INTERNAL PROGRAMMATIC DETAILS

This section is mainly relevant to the RBT DB implementation. It is

highly recommended that programmers using the RBT library stick to the

functions named in the previous section.

The dns_rbt_addname and dns_rbt_findname functions named in the

previous section are wrappers around dns_rbt_addnode and

dns_rbt_findnode. The *node functions for the most part do not

particularly care whether a node has an associated data pointer or

not, whereas the *name functions do. The one exception to this is

that when a PARTIALMATCH is returned for a search, the indicated node

is the deepest match that has data, rather than just the deepest

match. Even that behavior is selectable, however, using the boolean

empty_data_ok argument to dns_rbt_findnode.

Each node in the tree of trees is represented by the following structure:

typedef struct dns_rbtnode {

struct dns_rbtnode *left;

struct dns_rbtnode *right;

struct dns_rbtnode *down;

/*

* The following bitfields add up to a total bitwidth of 32.

* The range of values necessary for each item is indicated,

* but in the case of "attributes" the field is wider to accomodate

* possible future expansion. "offsetlen" could be one bit

* narrower by always adjusting its value by 1 to find the real

* offsetlen, but doing so does not gain anything (except perhaps

* another bit for "attributes", which doesn't yet need any more).

*/

unsigned int color:1; /* range is 0..1 */

unsigned int attributes:6; /* range is 0..2 */

unsigned int namelen:8; /* range is 1..255 */

unsigned int offsetlen:8; /* range is 1..128 */

unsigned int padbytes:9; /* range is 0..380 */

/*

* These values are used in the RBT DB implementation. The

* appropriate node lock must be held before accessing them.

*/

void *data;

unsigned int dirty:1;

unsigned int locknum:DNS_RBT_LOCKLENGTH;

unsigned int references:DNS_RBT_REFLENGTH;

} dns_rbtnode_t;

@@@