A Transaction-Friendy Binary Search Tree Tyler C RAIN Vincent G - - PowerPoint PPT Presentation

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A Transaction-Friendy Binary Search Tree Tyler C RAIN Vincent G - - PowerPoint PPT Presentation

Jan 21, 2024 230 likes •625 views

A Transaction-Friendy Binary Search Tree Tyler C RAIN Vincent G RAMOLI Michel R AYNAL { tyler.crain|raynal } @irisa.fr { vincent.gramoli } @epfl.ch TM Theory Workshop 2011 ASAP team, IRISA, Rennes, France & Distributed Programming Laboratory,

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A Transaction-Friendy Binary Search Tree

Tyler CRAIN Vincent GRAMOLI Michel RAYNAL {tyler.crain|raynal}@irisa.fr {vincent.gramoli}@epfl.ch

TM Theory Workshop 2011

ASAP team, IRISA, Rennes, France & Distributed Programming Laboratory, EPFL, Lausanne, Switzerland

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Existing Data Structures

Preserving structural invariants

  • Balanced Binary Trees
  • Rotations keep the tree balanced
  • Skiplist
  • Node levels follow some fixed distribution
  • Hashtable
  • Bucket size must not exceed some threshold

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Using data structures with TM

Simple!

  • Copy-paste into transactions (more or less)

+ Easy to program/use + The TM system ensures safety

  • Are there disadvantages?

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Concurrent Data Structures

Balanced Binary Tree

  • Specially designed for concurrency
  • Hand-over-hand locking
  • O(log n)

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Data Structures in TM (So far)

Balanced Binary Tree

  • (Mostly) Unmodified from their original versions
  • Not designed for concurrency or transactions
  • Could lead to unnecessary conflicts and aborts.
  • Ω(r log n)

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Ω(r log n)

What is r?

  • The number of restarts
  • Depends on the contention of the workload
  • Depends on the conflicts between transactions

⇒ r depends on n

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Aborts and wasted work

  • Still O(log n) operations?

Update 0% 10% 20% 30% 40% 50% AVL tree 29 415 711 1008 1981 2081 Sun red-black tree 31 573 965 1108 1484 1545

Table: Maximum #reads/op in 212 sized trees

  • Can we relax some invariants in order to reduce conflicts?

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Example

  • 3 operations
  • 1 → insert, 2 → delete, 3 → contains
  • 1

2 3

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Where they can conflict

  • Along their entire path
  • 1

2 3

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Goal

  • Minimize conflicts
  • 1

2 3

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Rotations

Correctness & Conflicts

  • Rotations are not required for correctness
  • There will be concurrent insertions/deletions
  • Concurrent insertions/deletions might have conflicting

rotations

  • They might cancel each other out
  • A later insert/deletion might invalidate these rotations
  • Idea: relax the balance requirement in order to allow more

concurrency

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Rotations cont.

Solution

  • Separate rotations from insert/delete operations
  • Perform rotations in their own thread
  • Each rotation is a single transaction

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Boug´ e L., Gabarro J., Messeguer X., Schabanel N., Height-relaxed AVL rebalancing: A unified, fine-grained approach to concurrent dictionaries. Tech Report RR1998-18, INRIA, 1998

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Deletions

Reducing conflicts further

  • A delete operation can still modify the tree structure
  • A successor must be found to replace the node being

deleted

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Deletions cont.

Solution

  • Logical deletions
  • Each node has a deleted boolean flag
  • Initialized as false
  • Set to true on deletion
  • Allows concurrent operations to traverse the node being

deleted without conflicting

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Removals

  • Logically deleted nodes must be removed from the tree
  • Done in a separate thread
  • Only nodes with 1 or 0 children are removed

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Bronson N., Casper J., Chafi H., Olukotun K., A Practical Concurrent Binary Search Tree, PPoPP ’10

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Contains

  • Each diagram is a single transaction

Traverse Traverse

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Insert

  • Each diagram is a single transaction

Traverse Rotate ... Rotate Insert

Performed in separate thread

Traverse Insert + Rotate Propogate + + + Rotate

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Delete

  • Each diagram is a single transaction

Traverse + Rotate Propogate + + Traverse Find Successor Remove/Swap Rotate Rotate ... Mark + Remove

Performed in separate thread

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Now we have

Abstract transaction conflicts

  • 1

2 3

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Impact on read size

Update 0% 10% 20% 30% 40% 50% AVL tree 29 415 711 1008 1981 2081 Sun red-black tree 31 573 965 1108 1484 1545 Tx-friendly tree 29 75 123 120 144 180

Table: Maximum #reads/op in 212 sized trees

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Conclusion

Benefits of a Transaction Friendly Data Structure

  • Improved Performance
  • No difference to the programmer using the tree as a library
  • Uses normal transactional reads/writes
  • Compatible with many TMs
  • Tested on TinySTM and E-STM
  • Independent of TM specifications
  • Tested using CTL/ETL, different contention managers

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Reusability

Move operation

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Future Work

Other structures

  • Transaction friendly skip list
  • Transaction friendly hash table
  • Transaction friendly . . .

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

  • There’s more?

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

TM Optimizations

Optional

  • Certain TMs give mechanisms for improved performance

at the cost of safety

  • Early-release
  • E-STM
  • View transactions
  • Unit reads

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Unit Reads

  • Returns the latest value written by a committed transaction
  • Does not add the location to the read set or perform

validation

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  • How can unit reads be used to improve performance of the

algorithm?

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Current Situation

  • Rotations can still conflict with concurrent

insert/delete/contains operations

  • Rotation 1

Rotation 2

1 2 3

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Solution

  • Use unit reads during the tree traversal
  • Advantages:
  • Faster traversals (unit reads are cheaper)
  • Avoid during traversal
  • Smaller read set

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Result

Abstract + Structural Transactions

  • Rotation 1

Rotation 2

1 2 4

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  • What about safety?
  • Algorithm becomes a bit more complicated to ensure

safety

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New rotations

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New removals

p j i i p j (a) Before removal NULL (b) After removal

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Traversals

  • Mostly unit reads
  • Transactional reads performed at bottom to ensure safety
  • Each node has a removed flag
  • Used to ensure traversal does not finish on a node that no

longer in the tree

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Impact on read size

Update 0% 10% 20% 30% 40% 50% AVL tree 29 415 711 1008 1981 2081 Sun red-black tree 31 573 965 1108 1484 1545 Tx-friendly tree 29 75 123 120 144 180 Unit read tree 2 5 6 13 15 18

Table: Maximum #reads/op in 212 sized trees

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

  • Performance Results: Some graphs from benchmarks

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Microbench

5 10 15 1 8 16 24 32 40 48 5% update Normal RBtree TFtree NRtree AVLtree 5 10 15 1 8 16 24 32 40 48 Bias 2 4 6 8 10 1 8 16 24 32 40 48 10% update 2 4 6 8 10 1 8 16 24 32 40 48 2 4 6 8 1 8 16 24 32 40 48 15% update Throughput (ops/microsec) 2 4 6 8 1 8 16 24 32 40 48 2 4 6 8 1 8 16 24 32 40 48 20% update Number of threads 2 4 6 8 1 8 16 24 32 40 48 Number of threads

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Data Structures Binary Trees Binary Search Tree for TM Conclusion Optional Optimizations Results

Vacation (STAMP)

1 2 3 4 5 6 7 1 8 16 24 32 40 48 10 20 30 40 50 60 70 1x transactions Vacation high contention RBtree speedup TFtree speedup NRtree speedup RBtree duration TFtree duration NRtree duration 1 2 3 4 5 6 7 1 8 16 24 32 40 48 10 20 30 40 50 Vacation low contention 1 2 3 4 5 6 1 8 16 24 32 40 48 200 400 600 800 1000 8x transactions Speedup 1 2 3 4 5 6 7 8 1 8 16 24 32 40 48 100 200 300 400 500 Duration (sec) 1 2 3 4 5 6 1 8 16 24 32 40 48 500 1000 1500 2000 2500 16x transactions Number of threads 1 2 3 4 5 6 7 8 9 1 8 16 24 32 40 48 500 1000 1500 Number of threads

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