Scalable and LockFree Concurrent Dictionaries

1
Scalable and Lock-Free Concurrent Dictionaries

• Håkan Sundell
• Philippas Tsigas

2
Outline

• Synchronization Methods
• Dictionaries
• Concurrent Dictionaries
• Previous results
• New Lock-Free Algorithm
• Experiments
• Conclusions

3
Synchronization

• Shared data structures needs synchronization
• Synchronization using Locks
• Mutually exclusive access to whole or parts of
  the data structure

P1
P2
P3
P1
P2
P3
4
Blocking Synchronization

• Drawbacks
• Blocking
• Priority Inversion
• Risk of deadlock
• Locks Semaphores, spinning, disabling interrupts
  etc.
• Reduced efficiency because of reduced parallelism

5
Non-blocking Synchronization

• Lock-Free Synchronization
• Optimistic approach (i.e. assumes no
  interference)
• The operation is prepared to later take effect
  (unless interfered) using hardware atomic
  primitives
• Possible interference is detected via the atomic
  primitives, and causes a retry
• Can cause starvation
• Wait-Free Synchronization
• Always finishes in a finite number of its own
  steps.

6
Dictionaries (Sets)

• Fundamental data structure
• Works on a set of ltkey,valuegt pairs
• Three basic operations
• Insert(k,v) Adds a new item
• vFindKey(k) Finds the item ltk,vgt
• vDeleteKey(k) Finds and removes the item ltk,vgt

7
Previous Non-blocking Dictionaries

• M. Michael High Performance Dynamic Lock-Free
  Hash Tables and List-Based Sets, SPAA 2002
• Based on Singly-Linked List
• Linear time complexity!
• Fast Lock-Free Memory Management
• Causes retries of concurrent search operations!
• Building-block of Hash Tables
• Assumes each branch is of length ltlt10.
• However, Hash Tables might not be uniformly
  distributed.

8
Randomized Algorithm Skip Lists

• William Pugh Skip Lists A Probabilistic
  Alternative to Balanced Trees, 1990
• Layers of ordered lists with different densities,
  achieves a tree-like behavior
• Time complexity O(log2N) probabilistic!

Head
Tail

25
50
1
2
3
4
5
6
7
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New Lock-Free Concurrent Skip List

• Define node state to depend on the insertion
  status at lowest level as well as a deletion flag
• Insert from lowest level going upwards
• Set deletion flag. Delete from highest level
  going downwards

1
2
3
4
5
6
7
D
D
D
D
D
D
D
3
2
1
p
3
2
1
p
D
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Overlapping operations on shared data
Insert 2
2

• Example Insert operation- which of 2 or 3 gets
  inserted?
• Solution Compare-And-Swap atomic
  primitiveCAS(ppointer to word, oldword,
  newword)booleanatomic do if p old then
  p new return true else return false

1
4
3
Insert 3
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Concurrent Insert vs. Delete operations
b)
1
4
2
a)

• Problem- both nodes are deleted!
• Solution (Harris et al) Use bit 0 of pointer to
  mark deletion status

Delete
3
Insert
b)
1
4
2

a)
c)
3
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New Lock-Free Dictionary - Techniques Summary

• Based on Skip Lists
• Treated as layers of ordered lists
• Uses CAS atomic primitive
• Lock-Free memory management
• IBM Freelists
• Reference counting (ValoisMichaelScott)
• Helping scheme
• Back-Off strategy
• All together proved to be linearizable

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Experiments

• Experiment with 1-30 threads performed on systems
  with 2 respective 64 cpus.
• Each thread performs 20000 operations, whereof
  the first total 50-10000 operations are Inserts,
  remaining are equally randomly distributed over
  Insert, FindKey and DeleteKeys.
• Fixed Skiplist maximum level of 10.
• Compare with implementation by Michael, using
  same scenarios.
• Averaged execution time of 50 experiments.

14
SGI Origin 2000, 64 cpus.
15
Linux Pentium II, 2 cpus
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Conclusions

• Our lock-free implementation also includes the
  value-oriented operations FindValue and
  DeleteValue.
• Our lock-free algorithm is suitable for both
  pre-emptive as well as systems with full
  concurrency
• Will be available as part of NOBLE software
  library, http//www.noble-library.org
• See Technical Report for full details,http//www.
  cs.chalmers.se/phs

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Questions?

• Contact Information
• Address Håkan Sundell vs. Philippas
  Tsigas Computing Science Chalmers University
  of Technology
• Email ltphs , tsigasgt _at_ cs.chalmers.se
• Web http//www.cs.chalmers.se/phs/wa
  rp

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Dynamic Memory Management

• Problem System memory allocation functionality
  is blocking!
• Solution (lock-free), IBM freelists
• Pre-allocate a number of nodes, link them into a
  dynamic stack structure, and allocate/reclaim
  using CAS

Allocate
Head
Mem 1
Mem 2
Mem n

Reclaim
Used 1
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The ABA problem

• Problem Because of concurrency (pre-emption in
  particular), same pointer value does not always
  mean same node (i.e. CAS succeeds)!!!

Step 1
1
7
6
4
Step 2
2
7
3
4
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The ABA problem

• Solution (Valois et al) Add reference counting
  to each node, in order to prevent nodes that are
  of interest to some thread to be reclaimed until
  all threads have left the node

1

6

New Step 2
1
1
CAS Failes!
2
7
3
?
?
?
4
1
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Helping Scheme

• Threads need to traverse safely
• Need to remove marked-to-be-deleted nodes while
  traversing Help!
• Finds previous node, finish deletion and
  continues traversing from previous node

or
1
4
2

1
4
2

?
?
1
4
2

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Back-Off Strategy

• For pre-emptive systems, helping is necessary for
  efficiency and lock-freeness
• For really concurrent systems, overlapping CAS
  operations (caused by helping and others) on the
  same node can cause heavy contention
• Solution For every failed CAS attempt, back-off
  (i.e. sleep) for a certain duration, which
  increases exponentially

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Non-blocking Synchronization

• Lock-Free Synchronization
• Avoids problems with locks
• Simple algorithms
• Fast when having low contention
• Wait-Free Synchronization
• Always finishes in a finite number of its own
  steps.
• Complex algorithms
• Memory consuming
• Less efficient in average than lock-free

24
Full SGI
25
Full Linux
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The algorithm in more detail

• Insert
• Create node with random height
• Search position (Remember drops)
• Insert or update on level 1
• Insert on level 2 to top (unless already deleted)
• If already deleted then HelpDelete(1)
• All of this while keeping track of references,
  help deleted nodes etc.

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The algorithm in more detail

• DeleteKey
• Search position (Remember drops)
• Mark node at level 1 as deleted, otherwise fail
• Mark next pointers on level 1 to top
• Delete on level top to 1 while detecting helping,
  indicate success
• Free node
• All of this while keeping track of references,
  help deleted nodes etc.

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The algorithm in more detail

• HelpDelete(level)
• Mark next pointer at level to top
• Find previous node (info in node)
• Delete on level unless already helped, indicate
  success
• Return previous node
• All of this while keeping track of references,
  help deleted nodes etc.

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Correctness

• Linearizability (Herlihy 1991)
• In order for an implementation to be
  linearizable, for every concurrent execution,
  there should exist an equal sequential execution
  that respects the partial order of the operations
  in the concurrent execution

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Correctness

• Define precise sequential semantics
• Define abstract state and its interpretation
• Show that state is atomically updated
• Define linearizability points
• Show that operations take effect atomically at
  these points with respect to sequential semantics
• Creates a total order using the linearizability
  points that respects the partial order
• The algorithm is linearizable

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Correctness

• Lock-freeness
• At least one operation should always make
  progress
• There are no cyclic loop depencies, and all
  potentially unbounded loops are gate-keeped by
  CAS operations
• The CAS operation guarantees that at least one
  CAS will always succeed
• The algorithm is lock-free