Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
Ctrie Data Structure
Search
Aleksandar Prokopec
February 28, 2012
Programming
0
200
Ctrie Data Structure
The description of the Ctrie data structure from PPoPP 2012.
Aleksandar Prokopec
February 28, 2012
Tweet
Share
More Decks by Aleksandar Prokopec
See All by Aleksandar Prokopec
ScalaMeter in 2014
axel22
0
310
Reactive Collections
axel22
0
190
A Reactive 3D Game Engine in Scala
axel22
4
8.2k
ScalaBlitz
axel22
0
200
Work-stealing Tree Scheduler
axel22
1
68
ScalaMeter
axel22
0
130
Parallel Collections Overview
axel22
0
100
Introduction to Scala
axel22
2
290
Other Decks in Programming
See All in Programming
プロダクト志向ってなんなんだろうね
righttouch
PRO
0
140
Beyond Portability: Live Migration for Evolving WebAssembly Workloads
chikuwait
0
390
たった 1 枚の PHP ファイルで実装する MCP サーバ / MCP Server with Vanilla PHP
okashoi
1
160
Webの外へ飛び出せ NativePHPが切り拓くPHPの未来
takuyakatsusa
1
240
DroidKnights 2025 - 다양한 스크롤 뷰에서의 영상 재생
gaeun5744
3
300
Datadog RUM 本番導入までの道
shinter61
1
310
今ならAmazon ECSのサービス間通信をどう選ぶか / Selection of ECS Interservice Communication 2025
tkikuc
14
2.9k
Result型で“失敗”を型にするPHPコードの書き方
kajitack
4
150
PHPで始める振る舞い駆動開発(Behaviour-Driven Development)
ohmori_yusuke
2
160
Azure AI Foundryではじめてのマルチエージェントワークフロー
seosoft
0
110
明示と暗黙 ー PHPとGoの インターフェイスの違いを知る
shimabox
2
210
ktr0731/go-mcpでMCPサーバー作ってみた
takak2166
0
170
Featured
See All Featured
Six Lessons from altMBA
skipperchong
28
3.8k
Unsuck your backbone
ammeep
671
58k
No one is an island. Learnings from fostering a developers community.
thoeni
21
3.3k
Understanding Cognitive Biases in Performance Measurement
bluesmoon
29
1.8k
BBQ
matthewcrist
89
9.7k
Bash Introduction
62gerente
614
210k
Keith and Marios Guide to Fast Websites
keithpitt
411
22k
Connecting the Dots Between Site Speed, User Experience & Your Business [WebExpo 2025]
tammyeverts
4
200
10 Git Anti Patterns You Should be Aware of
lemiorhan
PRO
657
60k
The Psychology of Web Performance [Beyond Tellerrand 2023]
tammyeverts
48
2.8k
I Don’t Have Time: Getting Over the Fear to Launch Your Podcast
jcasabona
32
2.3k
Visualizing Your Data: Incorporating Mongo into Loggly Infrastructure
mongodb
46
9.6k
Transcript
Concurrent Tries with Efficient Non-blocking Snapshots Aleksandar Prokopec Phil Bagwell
Martin Odersky École Polytechnique Fédérale de Lausanne Nathan Bronson Stanford
Motivation val numbers = getNumbers() // compute square roots numbers
foreach { entry => x = entry.root n = entry.number entry.root = 0.5 * (x + n / x) if (abs(entry.root - x) < eps) numbers.remove(entry) }
Hash Array Mapped Tries (HAMT)
Hash Array Mapped Tries (HAMT) 0 = 0000002
Hash Array Mapped Tries (HAMT) 0
Hash Array Mapped Tries (HAMT) 0 16 = 0100002
Hash Array Mapped Tries (HAMT) 0 16
Hash Array Mapped Tries (HAMT) 0 16 4 = 0001002
Hash Array Mapped Tries (HAMT) 16 0 4 = 0001002
Hash Array Mapped Tries (HAMT) 16 0 4
Hash Array Mapped Tries (HAMT) 16 0 4 12 =
0011002
Hash Array Mapped Tries (HAMT) 16 0 4 12 =
0011002
Hash Array Mapped Tries (HAMT) 16 0 4 12
Hash Array Mapped Tries (HAMT) 16 33 0 4 12
Hash Array Mapped Tries (HAMT) 16 33 0 4 12
48
Hash Array Mapped Tries (HAMT) 16 0 4 12 48
33 37
Hash Array Mapped Tries (HAMT) 16 4 12 48 33
37 0 3
Hash Array Mapped Tries (HAMT) 4 12 16 20 25
33 37 0 1 8 9 3 48 57
Immutable HAMT • used as immutable maps in functional languages
4 12 16 20 25 33 37 0 1 8 9 3
Immutable HAMT • updates rewrite path from root to leaf
4 12 16 20 25 33 37 0 1 8 9 3 4 12 8 9 11 insert(11)
Immutable HAMT • updates rewrite path from root to leaf
4 12 16 20 25 33 37 0 1 8 9 3 4 12 8 9 11 insert(11) efficient updates - logk (n)
Node compression 48 57 48 57 1 0 1 0
48 57 1 0 1 0 48 57 10 BITPOP(((1 << ((hc >> lev) & 1F)) – 1) & BMP)
Node compression 48 57 48 57 1 0 1 0
48 57 1 0 1 0 48 57 10 48 57
Ctrie Can mutable HAMT be modified to be thread-safe?
Ctrie insert 4 9 12 16 20 25 33 37
0 1 3 48 57 17 = 0100012
Ctrie insert 4 9 12 16 20 25 33 37
0 1 3 48 57 17 = 0100012 16 17 1) allocate
Ctrie insert 4 9 12 20 25 33 37 0
1 3 48 57 17 = 0100012 16 17 2) CAS
Ctrie insert 4 9 12 20 25 33 37 0
1 3 48 57 17 = 0100012 16 17
Ctrie insert 4 9 12 33 37 0 1 3
48 57 18 = 0100102 16 17 20 25
Ctrie insert 4 9 12 33 37 0 1 3
48 57 18 = 0100102 16 17 20 25 1) allocate 16 17 18
Ctrie insert 4 9 12 33 37 0 1 3
48 57 18 = 0100102 20 25 2) CAS 16 17 18
Ctrie insert 4 9 12 33 37 0 1 3
48 57 18 = 0100102 20 25 2) CAS 16 17 18 Unless…
Ctrie insert 4 9 12 33 37 0 1 3
48 57 18 = 0100102 16 17 20 25 T1-1) allocate 16 17 18 Unless… 28 = 0111002 T1 T2
Ctrie insert 4 9 12 0 1 3 18 =
0100102 16 17 20 25 T1-1) allocate 16 17 18 Unless… 28 = 0111002 T1 T2 20 25 28 T2-1) allocate
Ctrie insert 4 9 12 0 1 3 18 =
0100102 16 17 20 25 T1-1) allocate 16 17 18 28 = 0111002 T1 T2 20 25 28 T2-2) CAS
Ctrie insert 4 9 12 0 1 3 18 =
0100102 16 17 20 25 T1-2) CAS 16 17 18 28 = 0111002 T1 T2 20 25 28 T2-2) CAS
Ctrie insert 4 9 12 0 1 3 18 =
0100102 16 17 20 25 16 17 18 28 = 0111002 T1 T2 20 25 28 Lost insert!
Ctrie insert – 2nd attempt 4 9 12 0 1
3 16 17 20 25 Solution: I-nodes
Ctrie insert – 2nd attempt 4 9 12 0 1
3 16 17 20 25 18 = 0100102 28 = 0111002 T1 T2
Ctrie insert – 2nd attempt 4 9 12 0 1
3 16 17 T1 T2 20 25 18 = 0100102 28 = 0111002 16 17 18 20 25 28 T2-1) allocate T1-1) allocate
Ctrie insert – 2nd attempt 4 9 12 0 1
3 16 17 T1 T2 20 25 16 17 18 20 25 28 T2-2) CAS T1-2) CAS
Ctrie insert – 2nd attempt 4 9 12 0 1
3 16 17 18 20 25 28
Ctrie insert – 2nd attempt 4 9 12 0 1
3 16 17 18 20 25 28 Idea: once added to the Ctrie, I-nodes remain present.
Ctrie insert – 2nd attempt 4 9 12 0 1
3 16 17 18 20 25 28 Remove operation supported as well - details in the paper.
Ctrie size 4 9 12 0 1 3 16 17
18 20 25 28
Ctrie size 4 9 12 0 1 3 16 17
18 20 25 28 size = 0
Ctrie size 4 9 12 0 1 3 16 17
18 20 25 28 size = 0
Ctrie size 4 9 12 0 1 3 16 17
18 20 25 28 size = 0
Ctrie size 4 9 12 0 1 3 16 17
18 20 25 28 size = 0
Ctrie size 4 9 12 0 1 3 16 17
18 20 25 28 size = 1
Ctrie size 4 9 12 0 1 3 16 17
18 20 25 28 size = 2
Ctrie size 4 9 12 0 1 3 16 17
18 20 25 28 size = 3
Ctrie size 4 9 12 0 1 3 16 17
18 20 25 28 size = 5
Ctrie size 4 9 12 0 1 3 16 17
18 20 25 28 size = 5 actual size = 12
Ctrie size 4 9 12 0 1 3 16 17
18 20 25 28 size = 5 0 1 actual size = 12
Ctrie size 4 9 12 0 1 3 16 17
18 20 25 28 size = 5 0 1 CAS actual size = 11
Ctrie size 4 9 12 16 17 18 20 25
28 size = 5 0 1 actual size = 11
Ctrie size 4 9 12 16 17 18 20 25
28 size = 6 0 1 actual size = 11
Ctrie size 4 9 12 16 17 18 20 25
28 size = 6 0 1 actual size = 11 19
Ctrie size 4 9 12 16 17 18 20 25
28 size = 6 0 1 actual size = 11 16 17 18 19
Ctrie size 4 9 12 16 17 18 20 25
28 size = 6 0 1 actual size = 12 16 17 18 19 CAS
Ctrie size 4 9 12 20 25 28 size =
6 0 1 actual size = 12 16 17 18 19
Ctrie size 4 9 12 20 25 28 size =
6 0 1 actual size = 12 16 17 18 19
Ctrie size 4 9 12 20 25 28 size =
7 0 1 actual size = 9 16 17 18 19
Ctrie size 4 9 12 20 25 28 size =
8 0 1 actual size = 12 16 17 18 19
Ctrie size 4 9 12 20 25 28 size =
9 0 1 actual size = 12 16 17 18 19
Ctrie size 4 9 12 20 25 28 size =
10 0 1 actual size = 12 16 17 18 19
Ctrie size 4 9 12 20 25 28 size =
11 0 1 actual size = 12 16 17 18 19
Ctrie size 4 9 12 20 25 28 size =
12 0 1 actual size = 12 16 17 18 19
Ctrie size 4 9 12 20 25 28 size =
13 0 1 actual size = 12 16 17 18 19
Ctrie size 4 9 12 20 25 28 size =
13 0 1 actual size = 12 16 17 18 19 But the size was never 13!
Global state information 4 9 12 20 25 28 0
1 16 17 18 19 • size • find • filter • iterator
Global state information 4 9 12 20 25 28 0
1 16 17 18 19 • size • find • filter • iterator snapshot
Snapshot using locks 4 9 12 20 25 28 0
1 16 17 18 19
Snapshot using locks 4 9 12 20 25 28 0
1 16 17 18 19 • copy expensive
Snapshot using locks 4 9 12 20 25 28 0
1 16 17 18 19 • copy expensive • not lock-free
Snapshot using locks 4 9 12 20 25 28 0
1 16 17 18 19 • copy expensive • not lock-free • can insert or remove remain lock-free? 0 1 2 CAS
Snapshot using locks 4 9 12 20 25 28 0
1 16 17 18 19 • copy expensive • not lock-free • can insert or remove remain lock-free? 0 1 2 CAS
Snapshot using logs 4 9 12 20 25 28 0
1 16 17 18 19 • keep a linked list of previous values in each I-node
Snapshot using logs 4 9 12 20 25 28 0
1 16 17 18 19 0 1 2 • keep a linked list of previous values in each I-node
Snapshot using logs 4 9 12 20 25 28 0
1 16 17 18 19 • keep a linked list of previous values in each I-node • when is it safe to delete old entries? 0 1 2
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 root
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 root
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 snapshot! root
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 snapshot! #2 root 1) create new I-node at #2
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 snapshot! #2 root 2) set snapshot snapshot #1
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 snapshot! #2 root 3) CAS root to new I-node snapshot #1
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 subsequent insert #2 root snapshot #1 2
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 subsequent insert #2 root snapshot #1 2 generation #2 - ok!
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 subsequent insert #2 root snapshot #1 2 generation #1 not ok, too old!
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 subsequent insert #2 root 1) create updated node at #2 snapshot #1 2 #2 #2
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 subsequent insert #2 root 2) CAS to the updated node snapshot #1 2 #2 #2
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 subsequent insert #2 root snapshot #1 2 #2 #2 #1 too old!
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 subsequent insert #2 root snapshot #1 2 #2 #2 4 9 12 #2 1) create updated node at #2
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 subsequent insert #2 root snapshot #1 2 #2 #2 4 9 12 #2 2) CAS
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 subsequent insert #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 finally, create a new leaf and CAS
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 another insert #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 3
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 another insert #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 0 1 2 3
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 But... this won't really work... why? #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 0 1 2 3
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 0 1 2 3 T2: remove 19 16 17 18
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 0 1 2 3 T2: remove 19 16 17 18 CAS
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 0 1 2 3 T2: remove 19 16 17 18 CAS How to fail this last CAS?
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 0 1 2 3 T2: remove 19 16 17 18 DCAS How to fail this last CAS? DCAS
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 0 1 2 3 T2: remove 19 16 17 18 How to fail this last CAS? DCAS - software based DCAS
Snapshot using immutability 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 0 1 2 3 T2: remove 19 16 17 18 How to fail this last CAS? DCAS - software based ...creates intermediate objects DCAS
GCAS - generation-compare-and-swap 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 3 T2: remove 19 16 17 18 prev 1) set prev field
GCAS - generation-compare-and-swap 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 3 T2: remove 19 16 17 18 prev 2) CAS
GCAS - generation-compare-and-swap 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 3 T2: remove 19 16 17 18 prev 3) read root generation
GCAS - generation-compare-and-swap 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 3 16 17 18 prev 4) if root generation changed CAS prev to FailedNode(prev) FN
GCAS - generation-compare-and-swap 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 3 16 17 18 prev 4) if root generation changed CAS prev to FailedNode(prev) FN
GCAS - generation-compare-and-swap 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 3 16 17 18 prev 5) CAS to previous value FN
GCAS - generation-compare-and-swap 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 3 16 17 18 prev 4) if root generation unchanged CAS prev to null
GCAS - generation-compare-and-swap 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 3 16 17 18 4) if root generation unchanged CAS prev to null
GCAS - generation-compare-and-swap 4 9 12 20 25 28 0
1 16 17 18 19 #1 #1 #1 #1 #1 #2 root snapshot #1 #2 #2 4 9 12 #2 0 1 2 3 1) Replace all CAS with GCAS 2) Replace all READ with GCAS_READ (which checks if prev field is null)
Snapshot-based iterator def iterator = if (isSnapshot) new Iterator(root) else
snapshot().iterator()
Snapshot-based size def size = { val sz = 0
val it = iterator while (it.hasNext) sz += 1 sz }
Snapshot-based size def size = { val sz = 0
val it = iterator while (it.hasNext) sz += 1 sz } Above is O(n). But, by caching size in nodes - amortized O(logk n)! (see source code)
Snapshot-based atomic clear def clear() = { val or =
READ(root) val nr = new INode(new Gen) if (!CAS(root, or, nr)) clear() } (roughly)
Evaluation - quad core i7
Evaluation – UltraSPARC T2
Evaluation – 4x 8-core i7
Evaluation – snapshot
Conclusion • snapshots are linearizable and lock-free • snapshots take
constant time • snapshots are horizontally scalable • snapshots add a non-significant overhead to the algorithm if they aren't used • the approach may be applicable to tree-based lock-free data-structures in general (intuition)
Thank you!