1. Fractal Tree®
Technology Overview
The Art of Indexing
Martín Farach-Colton
Co-founder & Chief Technology Officer

2. The Art of Indexing
®
Not all indexing is the same
B-tree is the basis for almost all DB systems
• Data structure invented in 1972
• Has not kept up with hardware trends
‣ Works poorly on modern rotational disks
‣ Works poorly on SSD
Fractal Tree Indexes is the basis of TokuDB
• Scales with hardware
• Fast Indexing ➔ More Indexing ➔ Faster Queries
• Great Compression
• No Fragmentation
• Reduced wear on SSDs

3. How do Fractal Tree
Indexes outperform
B-trees?

4. How do Fractal Tree
Indexes outperform
B-trees?
First, some facts about storage systems

5. The Art of Indexing
®
Storage is quirky
Hard disks are slow for
random I/O but fast for
sequential I/O
Difference causes problems
like fragmentation, ...

6. The Art of Indexing
®
Storage is quirky
Hard disks are slow for
random I/O but fast for
sequential I/O
SSDs are fast for
random I/O but expensive for
sequential.
Garbage collection
causes artefacts: increased
wear, write cliffs...
Difference causes problems
like fragmentation, ...

7. The Art of Indexing
®
Storage ♡ Big Reads and Writes
Big I/Os

8. The Art of Indexing
®
Storage ♡ Big Reads and Writes
Big I/Os
Hard Disks: No
Fragmentation

9. The Art of Indexing
®
Storage ♡ Big Reads and Writes
Big I/Os
Hard Disks: No
Fragmentation SSDs: Less Garbage
Collection & Wear

10. The Art of Indexing
®
Storage ♡ Big Reads and Writes
Big I/Os
Hard Disks: No
Fragmentation SSDs: Less Garbage
Collection & Wear
But you only get the goodies if
each I/O has lots of new bytes

11. The Art of Indexing
®
Storage ♡ Big Reads and Writes
Big I/Os
Hard Disks: No
Fragmentation SSDs: Less Garbage
Collection & Wear
But you only get the goodies if
each I/O has lots of new bytes
If you read a big block, change one byte, then
write it, you get terrible wear problems

12. The Art of Indexing
®
Storage ♡ Big Reads and Writes
Big I/Os
Hard Disks: No
Fragmentation SSDs: Less Garbage
Collection & Wear
Both: Better
Compression
But you only get the goodies if
each I/O has lots of new bytes
If you read a big block, change one byte, then
write it, you get terrible wear problems

13. The Art of Indexing
®
Caching is great
• But you can’t cache all your data
• For stuff not in memory, you have to go to disk
Goal: Do the best we can for the stuff on disk
Data is big, RAM is Small
Data
RAM

14. Now, What’s a B-tree?
& a Fractal Tree Index

15. The Art of Indexing
®
What’s a B-tree?
B
B B B... ...
B B……………………………………………….………….
Search Tree

16. The Art of Indexing
®
What’s a B-tree?
B
B B B... ...
B B……………………………………………….………….
Each node has B pivots
Search Tree

17. The Art of Indexing
®
What’s a B-tree?
B
B B B... ...
B B……………………………………………….………….
Each node has B pivots
Search Tree
Fetching pivots as a group
saves I/Os

18. The Art of Indexing
®
What’s a B-tree?
B
B B B... ...
B B……………………………………………….………….
Each node has B pivots
Search Tree
Fetching pivots as a group
saves I/Os
Most leaves are on disk, not in RAM

19. The Art of Indexing
®
What’s a B-tree?
B
B B B... ...
B B……………………………………………….………….
Each node has B pivots
Search Tree
Fetching pivots as a group
saves I/Os
Most leaves are on disk, not in RAM Inserting into a leaf that’s not in memory
will require an I/O per insertion

20. The Art of Indexing
®
B-tree Delivery Service
If fast memory is like walking across a room
• Each update in a B-tree is a walking trip from
‣ New York

21. The Art of Indexing
®
B-tree Delivery Service
If fast memory is like walking across a room
• Each update in a B-tree is a walking trip from
‣ New York to St Louis

22. The Art of Indexing
®
B-tree Delivery Service
If fast memory is like walking across a room
• Each update in a B-tree is a walking trip from
‣ New York to St Louis
Each item gets its own round trip!

23. The Art of Indexing
®
Real-world delivery
Keep regional warehouses
• Only move stuff when you can move a lot

24. The Art of Indexing
®
Real-world delivery
Keep regional warehouses
• Only move stuff when you can move a lot
Each item gets moved several times

25. The Art of Indexing
®
Real-world delivery
Keep regional warehouses
• Only move stuff when you can move a lot
Each item gets moved several times
But each trip is vastly cheaper

26. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers

27. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers

28. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers

29. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

30. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

31. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

32. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

33. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

34. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

35. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

36. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

37. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

38. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

39. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

40. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

41. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

42. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

43. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

44. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive

45. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive
Flush a buffer
when it fills

46. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive
Flush a buffer
when it fills
A flush might take an I/O, but it
does lots of useful work

47. The Art of Indexing
®
Fractal Tree Indexes
B
B B BB
Each node has
pivots & Buffers
Buffers fill as
updates arrive
Flush a buffer
when it fills
A flush might take an I/O, but it
does lots of useful work
More changes per write ➔
fewer changes for same write
load ➔ less SSD wear

48. The Art of Indexing
®
Fractal Tree Indexes: Queries
B
B B BB
Lots of buffers have
messages

49. The Art of Indexing
®
Fractal Tree Indexes: Queries
B
B B BB
Lots of buffers have
messages
But query follows
root-leaf path

50. The Art of Indexing
®
Fractal Tree Indexes: Queries
B
B B BB
Lots of buffers have
messages
But query follows
root-leaf path
So every query has the
most up-to-date information

51. The Art of Indexing
®
Fractal Tree Indexes: Queries
B
B B BB
Lots of buffers have
messages
But query follows
root-leaf path
So every query has the
most up-to-date information
Messages can be
insert, update, delete

52. The Art of Indexing
®
Fractal Tree Indexes: Schema Changes
B
B B BB
Schema Changes are
broadcast messages

53. The Art of Indexing
®
Fractal Tree Indexes: Schema Changes
B
B B BB
Schema Changes are
broadcast messages

54. The Art of Indexing
®
Fractal Tree Indexes: Schema Changes
B
B B BB
Schema Changes are
broadcast messages

55. The Art of Indexing
®
Fractal Tree Indexes: Schema Changes
B
B B BB
Schema Changes are
broadcast messages
Insertion into root is fast,
changes are immediate

56. The Art of Indexing
®
Fractal Tree Indexes: Schema Changes
B
B B BB
Schema Changes are
broadcast messages
Leaves get rewritten
when broadcast message
makes it that far
Insertion into root is fast,
changes are immediate
Schema change
message still on root-
leaf path

57. The Art of Indexing
®
Analysis
Delivery system gives goodies:
• Messages get moved, but each I/O pays for a lot of
movement
• You get very fast inserts
• You get Hot Schema Changes
Each flush carries lots of useful information
• So it’s worth it to make nodes big
• No fragmentation, Better Compression
• Much better wear on SSDs