Content Addressable Memory Using B-Tree Jack Dennis MIT Computer - - PowerPoint PPT Presentation

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Content Addressable Memory Using B-Tree Jack Dennis MIT Computer Science and Artificial Intelligence Laboratory 13 April 2008 1 Multi-Thread, Multi-Core Chip Instr Association Data Association Thread Scheduler CAM CAM MTP MTP MTP

SLIDE 1

13 April 2008 1

Content Addressable Memory Using B-Tree

Jack Dennis MIT Computer Science and Artificial Intelligence Laboratory

SLIDE 2

13 April 2008 2

Multi-Thread, Multi-Core Chip

IAU

Instruction Access Net

Shared Memory System Interface IAU DAU DAU

Data Access Net

MTP MTP MTP MTP

Data Association CAM Thread Scheduler Instr Association CAM

SLIDE 3

13 April 2008 3

Data Structures: The Heap as a DAG

Fan-out as large as 16

Leaf Chunks Root Chunk

Three levels yields 4096

elements (longs)

Cycle-Free Heap
Arrays as Trees

SLIDE 4

13 April 2008 4

B-Trees

A Data Structure that represents a collection of keys In an Order Z B-Tree, each node holds at least Z keys and associated pointers to subtrees. An order Z B-Tree of depth h can hold at least (Zh * 2) – 1 keys

SLIDE 5

13 April 2008 5

A B-Tree Node

Invariants (Order Z B-Tree; Z = 8 above):

ki k15 k0

k < k0 ki > k > ki+1 k > k15

ki+1 p0 pi p16

Number of keys at a node: at least Z; at most Z*2 Exception: The root node may contain as few as zero keys. All subtree pointers in a leaf node are null (and only those) All leaf nodes are at the same level.

SLIDE 6

13 April 2008 6

A Hardware B-Tree CAM

stunt box pointers compare keys > = < pointer to next node pointer index [0..16] pointers compare keys > = < M15 pointers M16 key M0 M U X match

SLIDE 7

13 April 2008 7

Insert

1. Search the B-Tree for the new key; failure if

found.

2. If the leaf node is full it must be split into two

nodes, each holding Z keys. The median key of the set of keys held by the found leaf node and the key to be inserted is inserted into the parent node, continuing up the tree.

3. To do insert in a single pass, split any full node

encountered during the search to anticipate the need.

SLIDE 8

13 April 2008 8

Delete

1. Search the B-Tree for the given key; failure if

not found.

2. To do delete a key from a leaf node, it may be

necessary to move in a key from a neighboring node; if this is not possible, the leaf node may be joined with one of its neighbors and the pointer to the lost node deleted from the parent

3. A few more complications arise.

SLIDE 9

13 April 2008 9

B-Tree Node Rearrangement

pointers keys pointers keys M15 pointers M16 M0 pointers keys M15 M0 Switch Split/Join read write pointers keys pointers M16 new key, pointer