Cuckoo Hashing for Storage Systems Yuanyuan Sun, Yu Hua, Zhangyu - - PowerPoint PPT Presentation

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Cuckoo Hashing for Storage Systems Yuanyuan Sun, Yu Hua, Zhangyu - - PowerPoint PPT Presentation

Dec 02, 2023 291 likes •983 views

Mitigating Asymmetric Read and Write Costs in Cuckoo Hashing for Storage Systems Yuanyuan Sun, Yu Hua, Zhangyu Chen, Yuncheng Guo Huazhong University of Science and Technology USENIX ATC 2019 Query Services in Cloud Storage Systems Large

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Mitigating Asymmetric Read and Write Costs in Cuckoo Hashing for Storage Systems

Yuanyuan Sun, Yu Hua, Zhangyu Chen, Yuncheng Guo Huazhong University of Science and Technology

USENIX ATC 2019

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SLIDE 2
  • Large amounts of data
  • 300 new profiles and more than 208 thousand photos per minute [September

2018@Facebook]

Query Services in Cloud Storage Systems

…

2

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SLIDE 3
  • Large amounts of data
  • 300 new profiles and more than 208 thousand photos per minute [September

2018@Facebook]

Query Services in Cloud Storage Systems

Demanding the support of low-latency and high-throughput queries …

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SLIDE 4

 Constant-scale read performance

  • Widely used in key-value stores and relational databases

Hash structures

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SLIDE 5

 Constant-scale read performance

  • Widely used in key-value stores and relational databases

ꭗ High latency for handling hash collisions

Hash structures

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SLIDE 6
  • Multi-choice hashing
  • Handling hash collisions: kick-out operations

Cuckoo Hashing

a n k m b T1 T2

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SLIDE 7
  • Multi-choice hashing
  • Handling hash collisions: kick-out operations

Cuckoo Hashing

Insert(x)

a n k m b T1 T2

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SLIDE 8
  • Multi-choice hashing
  • Handling hash collisions: kick-out operations

Cuckoo Hashing

a n k m b T1 T2 x

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SLIDE 9
  • Multi-choice hashing
  • Handling hash collisions: kick-out operations
  • For reads, only limited positions are probed => O(1) time complexity

Cuckoo Hashing

a n k b T1 T2 f m c

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SLIDE 10
  • Multi-choice hashing
  • Handling hash collisions: kick-out operations
  • For reads, only limited positions are probed => O(1) time complexity

Cuckoo Hashing

a n k b T1 T2 f m c

Find(c)

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SLIDE 11
  • Multi-choice hashing
  • Handling hash collisions: kick-out operations
  • For reads, only limited positions are probed => O(1) time complexity
  • For writes, endless loops may occur! => slow-write performance

Cuckoo Hashing

a n k b T1 T2 f m c a n f m c

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SLIDE 12
  • Multi-choice hashing
  • Handling hash collisions: kick-out operations
  • For reads, only limited positions are probed => O(1) time complexity
  • For writes, endless loops may occur! => slow-write performance

Cuckoo Hashing

a n k b T1 T2 f m c

Insert(x)

a n f m c

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SLIDE 13
  • Multi-choice hashing
  • Handling hash collisions: kick-out operations
  • For reads, only limited positions are probed => O(1) time complexity
  • For writes, endless loops may occur! => slow-write performance

Cuckoo Hashing

a n k b T1 T2 f m c

Insert(x)

a n f m c

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SLIDE 14
  • Multi-choice hashing
  • Handling hash collisions: kick-out operations
  • For reads, only limited positions are probed => O(1) time complexity
  • For writes, endless loops may occur! => slow-write performance

Cuckoo Hashing

a n k b T1 T2 f m c

Insert(x)

a n f m c

x

An endless loop occurs! 14

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SLIDE 15
  • Multi-choice hashing
  • Handling hash collisions: kick-out operations
  • For reads, only limited positions are probed => O(1) time complexity
  • For writes, endless loops may occur! => slow-write performance

Cuckoo Hashing

a n k b T1 T2 f m c

Insert(x)

a n f m c

x

An endless loop occurs!

Bottleneck: Asymmetric reads and writes!

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  • Existing concurrency strategy for cuckoo hashing
  • Lock two buckets before each kick-out operation (libcuckoo@EuroSys’14)

Concurrency in Multi-core Systems

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  • Existing concurrency strategy for cuckoo hashing
  • Lock two buckets before each kick-out operation (libcuckoo@EuroSys’14)
  • Challenges:
  • Inefficient insertion performance
  • Limited scalability

Concurrency in Multi-core Systems

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  • Existing concurrency strategy for cuckoo hashing
  • Lock two buckets before each kick-out operation (libcuckoo@EuroSys’14)
  • Challenges:
  • Inefficient insertion performance
  • Limited scalability
  • Design goal:
  • A high-throughput and concurrency-friendly cuckoo hash table

Concurrency in Multi-core Systems

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  • Pseudoforests to predetermine endless loops
  • Efficient concurrency strategy
  • A graph-grained locking mechanism
  • Concurrency optimization to reduce the length of critical path
  • Higher throughput than state-of-the-art scheme, i.e., libcuckoo

Our Approach: CoCuckoo

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  • Vertex: a bucket
  • Edge: an inserted item from the storage vertex to its backup vertex
  • Identify endless loops: #Vertices = #Edges (called maximal)

Pseudoforest

a n k b T1 T2 f m c

Insert(y)

a n k b f m c

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SLIDE 21
  • Vertex: a bucket
  • Edge: an inserted item from the storage vertex to its backup vertex
  • Identify endless loops: #Vertices = #Edges (called maximal)

Pseudoforest

a n k b T1 T2 f m c

Insert(y)

a n k b f m c

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SLIDE 22
  • Vertex: a bucket
  • Edge: an inserted item from the storage vertex to its backup vertex
  • Identify endless loops: #Vertices = #Edges (called maximal)

Pseudoforest

a n k b T1 T2 f m c

Insert(y)

a n k b f m c

Maximal

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SLIDE 23
  • Vertex: a bucket
  • Edge: an inserted item from the storage vertex to its backup vertex
  • Identify endless loops: #Vertices = #Edges (called maximal)

Pseudoforest

a n k b T1 T2 f m c

Insert(y)

a n k b f m c

Vacancy Maximal Non-maximal

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SLIDE 24
  • Vertex: a bucket
  • Edge: an inserted item from the storage vertex to its backup vertex
  • Identify endless loops: #Vertices = #Edges (called maximal)

Pseudoforest

a n k b T1 T2 f m c

Insert(y)

a n k b f m c

Maximal Non-maximal Vacancy

y y

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  • Vertex: a bucket
  • Edge: an inserted item from the storage vertex to its backup vertex
  • Identify endless loops: #Vertices = #Edges (called maximal)

Pseudoforest

a n k b T1 T2 f m c a n k b f m c y y

Maximal

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  • EMPTY subgraph: buckets not represented in pseudoforest

Graph-grained Locking

a n k b T1 T2 f m c a n k b f m c a n k b f m c

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  • EMPTY subgraph: buckets not represented in pseudoforest

Graph-grained Locking

a n k b T1 T2 f m c a n k b f m c a n k b f m c

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  • EMPTY subgraph: buckets not represented in pseudoforest
  • Classify insertions into 3 cases, which include 6 subcases

Graph-grained Locking

EMPTY Non-maximal Maximal

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  • EMPTY subgraph: buckets not represented in pseudoforest
  • Classify insertions into 3 cases, which include 6 subcases

Graph-grained Locking

TwoEmpty OneEmpty ZeroEmpty

According to the number of corresponding EMPTY subgraphs

/

EMPTY Non-maximal Maximal

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  • EMPTY subgraph: buckets not represented in pseudoforest
  • Classify insertions into 3 cases, which include 6 subcases

Graph-grained Locking

TwoEmpty OneEmpty ZeroEmpty Diff_non_non Same_non Diff_non_max Max

According to the number of corresponding EMPTY subgraphs According to the states and the number of subgraphs

/ /

EMPTY Non-maximal Maximal

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  • Two EMPTY subgraphs

TwoEmpty

T1 T2

Before insertion

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  • Two EMPTY subgraphs
  • Insertion algorithm:

Atomically assign allocated subgraph number to two buckets Insert item Mark the subgraph as non-maximal

TwoEmpty

T1 T2

Before insertion

critical path With graph-grained lock(s) Out of the critical path

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  • Two EMPTY subgraphs
  • Insertion algorithm:

Atomically assign allocated subgraph number to two buckets Insert item Mark the subgraph as non-maximal

TwoEmpty

a k T1 T2 f

Before insertion After insertion

critical path With graph-grained lock(s) Out of the critical path

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  • One EMPTY subgraph (the other is non-maximal/maximal)

OneEmpty /

a k T1 T2 f

/

Before insertion

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  • One EMPTY subgraph (the other is non-maximal/maximal)
  • Insertion algorithm:

 Two atomic operations without locks

  • Assign the existing subgraph number to the new vertex
  • Insert the item into the new vertex

OneEmpty /

a n k b T1 T2 f

/ /

Before insertion After insertion

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SLIDE 36
  • Two different non-maximal subgraphs
  • Insertion algorithm:

Kick-out (with item insertion) Merge two subgraphs

ZeroEmpty (Diff_non_non)

a n k b T1 T2 f

Insert(c)

a n f

Before insertion

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SLIDE 37
  • Two different non-maximal subgraphs
  • Insertion algorithm:

Kick-out (with item insertion) Merge two subgraphs

ZeroEmpty (Diff_non_non)

a n k b T1 T2 f

Insert(c)

a n f

Before insertion

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  • Two different non-maximal subgraphs
  • Insertion algorithm:

Kick-out (with item insertion) Merge two subgraphs

ZeroEmpty (Diff_non_non)

a n k b T1 T2 f

Insert(c)

a n f

Non-maximal Non-maximal Before insertion

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  • Two different non-maximal subgraphs
  • Insertion algorithm:

Kick-out (with item insertion) Merge two subgraphs

ZeroEmpty (Diff_non_non)

a n k b T1 T2 f c c a n f

Non-maximal Before insertion

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  • Two different non-maximal subgraphs
  • Insertion algorithm:

Kick-out (with item insertion) Merge two subgraphs

ZeroEmpty (Diff_non_non)

a n k b T1 T2 f c c a n f

Non-maximal Before insertion After insertion

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  • The same non-maximal subgraph
  • Insertion algorithm:

Mark as maximal

 Kick-out (with item insertion)

ZeroEmpty (Same_non)

a n k b T1 T2 f c

Insert(m)

a n f c

Before insertion

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  • The same non-maximal subgraph
  • Insertion algorithm:

Mark as maximal

 Kick-out (with item insertion)

ZeroEmpty (Same_non)

a n k b T1 T2 f c

Insert(m)

a n f c

Before insertion

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  • The same non-maximal subgraph
  • Insertion algorithm:

Mark as maximal

 Kick-out (with item insertion)

ZeroEmpty (Same_non)

a n k b T1 T2 f c

Insert(m) Non-maximal

a n f c

Before insertion

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  • The same non-maximal subgraph
  • Insertion algorithm:

Mark as maximal

 Kick-out (with item insertion)

ZeroEmpty (Same_non)

a n k b T1 T2 f c

Insert(m) Maximal

a n f c

Before insertion

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  • The same non-maximal subgraph
  • Insertion algorithm:

Mark as maximal

 Kick-out (with item insertion)

ZeroEmpty (Same_non)

a n k b T1 T2 f c

Insert(m) Maximal

a n f c

Before insertion

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  • The same non-maximal subgraph
  • Insertion algorithm:

Mark as maximal

 Kick-out (with item insertion)

ZeroEmpty (Same_non)

a n k b T1 T2 f c m m

Maximal

a n f c

Before insertion After insertion

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  • One non-maximal subgraph and one maximal subgraph
  • Insertion algorithm (similar to same_non):

Mark as maximal

 Kick-out (with item insertion)  Merge two subgraphs

ZeroEmpty (Diff_non_max)

a n k b T1 T2 f m c a n k b f m c

Insert(y)

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  • One non-maximal subgraph and one maximal subgraph
  • Insertion algorithm (similar to same_non):

Mark as maximal

 Kick-out (with item insertion)  Merge two subgraphs

ZeroEmpty (Diff_non_max)

a n k b T1 T2 f m c a n k b f m c

Insert(y)

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  • One non-maximal subgraph and one maximal subgraph
  • Insertion algorithm (similar to same_non):

Mark as maximal

 Kick-out (with item insertion)  Merge two subgraphs

ZeroEmpty (Diff_non_max)

a n k b T1 T2 f m c

Maximal Non-maximal

a n k b f m c

Insert(y)

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  • One non-maximal subgraph and one maximal subgraph
  • Insertion algorithm (similar to same_non):

Mark as maximal

 Kick-out (with item insertion)  Merge two subgraphs

ZeroEmpty (Diff_non_max)

a n k b T1 T2 f m c a n k b f m c

Maximal Insert(y)

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  • One non-maximal subgraph and one maximal subgraph
  • Insertion algorithm (similar to same_non):

Mark as maximal

 Kick-out (with item insertion)  Merge two subgraphs

ZeroEmpty (Diff_non_max)

a n k b T1 T2 f m c a n k b f m c

Maximal Insert(y)

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  • One non-maximal subgraph and one maximal subgraph
  • Insertion algorithm (similar to same_non):

Mark as maximal

 Kick-out (with item insertion)  Merge two subgraphs

ZeroEmpty (Diff_non_max)

a n k b T1 T2 f m c a n f m c

Maximal

y y b k

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  • Two maximal subgraphs or the same maximal subgraph
  • Always walking into a loop and predetermined to be a failure
  • Insertion algorithm:

 Do nothing

ZeroEmpty (Max) /

a n k b T1 T2 f m c

Insert(x)

a n f m c

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  • Two maximal subgraphs or the same maximal subgraph
  • Always walking into a loop and predetermined to be a failure
  • Insertion algorithm:

 Do nothing

ZeroEmpty (Max) /

a n k b T1 T2 f m c

Insert(x)

a n f m c

x Maximal

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  • Two maximal subgraphs or the same maximal subgraph
  • Always walking into a loop and predetermined to be a failure
  • Insertion algorithm:

 Do nothing

ZeroEmpty (Max) /

a n k b T1 T2 f m c

Insert(x)

a n f m c

x Maximal

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  • Most subgraphs are small

the granularity of graph-grained locks is acceptable

  • Only constraining a very small number of buckets
  • 3 vertices (44.25% subgraphs)
  • No more than 10 vertices (99% subgraphs)

Lock Granularity

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  • Subgraph number allocation
  • Subgraph number: identifying a unique subgraph
  • Unique without the need of continuity
  • Subgraph number generator: a simple modular function
  • Modulus: the total number of threads p
  • Remainder: the number of each thread r
  • n = kp+r , e.g., 8-thread CoCuckoo, Thread 2, n=2,10,18,…

Subgraph Management

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  • Comparison:
  • libcuckoo@EuroSys’14
  • Slot numbers: 1, 2, 4, 8, 16
  • Workloads:
  • YCSB: https://github.com/brianfrankcooper/YCSB @SOCC’11
  • 2 million key-value pairs per workload
  • Threads: 1, 4, 8, 12, 16
  • Metrics:
  • Throughput
  • Predetermination for insertion
  • Extra space overhead

Performance Evaluation

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  • CoCuckoo significantly increases average throughputs.
  • 75%-150% improvements compared to 2-way libcuckoo.

Average Insertion Throughput

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Predetermination for Insertion

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  • TwoEmpty and OneEmpty account for a large proportion
  • Short-term or no locks for the shared buckets

Predetermination for Insertion

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  • TwoEmpty and OneEmpty account for a large proportion
  • Short-term or no locks for the shared buckets
  • Max:
  • Predetermine insertion failures and release locks without any kick-out operations

Predetermination for Insertion

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Extra Space Overhead

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  • The same space available for both libcuckoo and CoCuckoo
  • CoCuckoo increases the throughput over 2-way libcuckoo by 73% - 159%.
  • CoCuckoo significantly decreases the average execution time per request.

Extra Space Overhead

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  • The same space available for both libcuckoo and CoCuckoo
  • CoCuckoo increases the throughput over 2-way libcuckoo by 73% - 159%.
  • CoCuckoo significantly decreases the average execution time per request.
  • The extra space overhead is small

Extra Space Overhead

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  • CoCuckoo mitigates the asymmetric read and write costs in cuckoo

hashing via

  • A pseudoforest to predetermine and avoid occurrence of endless

loops

  • Graph-grained locking mechanism and concurrency optimization
  • CoCuckoo achieves 75%-150% write throughput improvements

compared with 2-way libcuckoo.

Conclusion

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SLIDE 67

Q&A

https://csunyy.github.io/ Homepage::

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