1. Lecture 1: Introduction
Efficient Transformation of Obstruction-free Algorithms into Non-blocking Algorithms
Gadi Taubenfeld
Obstruction-freedom
Non-blocking
Wait-freedom
DISC 2007
Gadi Taubenfeld © Sept. 2007
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

2. Lecture 1: Introduction
Efficient Transformation of Obstruction-free Algorithms into Non-blocking Algorithms
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Thanks and enjoy!
Gadi Taubenfeld
All material copyright 2007
Gadi Taubenfeld, All Rights Reserved
To get the most updated version of these slides go to:
DISC 2007
Gadi Taubenfeld © Sept. 2007
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

3. Lock-based Data StructuresP1 P2 P3 P4
Entry
Critical Section
Sequential Data Structure
Exit
Sequential Bottleneck
fault-free solution only
locks are the de facto mechanism for concurrency control !
DISC 2007
Gadi Taubenfeld © Sept. 2007

4. Lock-free Data Structures
Lecture 1: Introduction
Lock-free Data Structures
Obstruction-freedom
Non-blocking
Wait-freedom
Fault-tolerant solutions
DISC 2007
Gadi Taubenfeld © Sept. 2007
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

5. Obstruction-freedom P1 P2 P3 P4 Done DISC 2007
Gadi Taubenfeld © Sept. 2007

6. Lecture 1: Introduction
Obstruction-freedom P1 P2 P3 P4
Instruction: click only after process 2 (the slowest) completes one round,
otherwise the transition will not be not smooth.
DISC 2007
Gadi Taubenfeld © Sept. 2007
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

7. Lecture 1: Introduction
Non-blocking P1 P2 P3 P4
Instruction: click only after process 3 (the slowest) completes *exectly* one round,
in order for the transition to be smooth.
Done
DISC 2007
Gadi Taubenfeld © Sept. 2007
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

8. Lecture 1: Introduction
Non-blocking P1 P2 P3 P4
Instruction: click only after process 2 (the slowest) completes one round,
otherwise the transition will not be not smooth.
DISC 2007
Gadi Taubenfeld © Sept. 2007
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

9. Lecture 1: Introduction
Wait-freedom P1 P2 P3 P4
Instruction: click only after process 2 (the slowest) completes one round,
otherwise the transition will not be not smooth.
DISC 2007
Gadi Taubenfeld © Sept. 2007
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

10. Lecture 1: Introduction
Wait-freedom P1 P2 P3 P4
Done
Done
Done
Done
DISC 2007
Gadi Taubenfeld © Sept. 2007
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

11. Lock-free Data Structures
Lecture 1: Introduction
Lock-free Data Structures
Obstruction-freedom
Non-blocking
Wait-freedom
too weak progress condition
not complex
strong enough
not so complex
strong/desirable
complex/less efficient
DISC 2007
Gadi Taubenfeld © Sept. 2007
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

12. Transformations & Results
Lecture 1: Introduction
Transformations & Results
Obstruction-freedom
The FLMS Transformation
wait-freedom
non-blocking
New
DISC 2005:
Faith Ellen Fich, Victor Luchangco, Mark Moir, Nir Shavit
Space: 2n registers + 1 fetch&increment object
Our results:
Define a time complexity measure
Show that the FLMS Transformation is exponential
New transformations with O(1) time complexity
Space: n registers + 1 compare&swap object
DISC 2007
Gadi Taubenfeld © Sept. 2007
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

13. Transformations & Results
Lecture 1: Introduction
Transformations & Results
Obstruction-freedom
Exponential
wait-freedom
non-blocking
O(1) ?
Open: Is there an efficient transformation?
DISC 2007
Gadi Taubenfeld © Sept. 2007
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

14. Unknown-bound semi-synchronous model
Lecture 1: Introduction
Unknown-bound semi-synchronous model
There is an unknown bound on memory access time, or
Some unknown bound exists on the relative execution
rates of any two processes.
All practical system satisfy the unknown-bound assumption.
 A process can delay itself for increasingly longer periods, and by doing so it can ensures that other processes will take enough steps.
DISC 2007
Gadi Taubenfeld © Sept. 2007
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

15. Lecture 1: Introduction
Time complexity
(Synchronization complexity)
Obstruction-freedom
wait-freedom
non-blocking
The FLMS Transformation
New
Given an algorithm divide its steps into three disjoint sets:
A – synchronization steps;
B – real work steps;
C – inexpensive steps.
Mutual exclusion
A – entry + exit ;
B – critical section;
C – all other steps.
Transformations:
A – access to shared memory ;
B – steps of the obstruction-free alg ;
C – all other steps.
DISC 2007
Gadi Taubenfeld © Sept. 2007
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

16. Lecture 1: Introduction
Time complexity P1 P2
A process is enabled if its next step or its last step is from B.
The max # of steps from A that a process need to take until it becomes enabled since the last time some process has been enabled.
time
Given an algorithm divide it steps …
A – synchronization steps;
B – real work steps;
C – inexpensive steps.
A single run
DISC 2007
Gadi Taubenfeld © Sept. 2007
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

17. The time complexity of the FLMS transformation
Lecture 1: Introduction
The time complexity of the FLMS transformation
Obstruction-freedom
The FLMS Transformation
wait-freedom P1 P2 Pn
no process is enabled
Pn accesses the shared memory at least 2n-1 x n times in this interval.
Pn is enabled
. . .
time
A single run
DISC 2007
Gadi Taubenfeld © Sept. 2007
Synchronization Algorithms and Concurrent Programming Gadi Taubenfeld © 2006

18. Our Transformation P1 P2 Obstruction-free algorithm Entry
Many ideas are from the FLMS paper! P1 P2
We start by assuming a fault-free-model
Can use a single lock
Expensive when there is no contention
Obstruction-free
algorithm
Entry
Critical Section
Exit
Obstruction-free
algorithm
DISC 2007
Gadi Taubenfeld © Sept. 2007

19. Our Transformation P1 P2 Obstruction-free algorithm Entry
Many ideas are from the FLMS paper! P1 P2
We start by assuming a fault-free-model
Can use a single lock
Expensive when there is no contention
Obstruction-free
algorithm
Tries for X steps …
Entry
Critical Section
Exit
Obstruction-free
algorithm
DISC 2007
Gadi Taubenfeld © Sept. 2007

20. Our Transformation P1 P2 Obstruction-free algorithm Entry
Many ideas are from the FLMS paper! P1 P2
We start by assuming a fault-free-model
Can use a single lock
Expensive when there is no contention
Obstruction-free
algorithm
Tries for X steps …
Problem?
Entry
Critical Section
Exit
No problem.
Obstruction-free
algorithm
DISC 2007
Gadi Taubenfeld © Sept. 2007

21. Observation Obstruction-freedom is useful even when using locking!
algorithm
Entry
Critical Section
Exit
Entry
Critical Section
Exit
Sequential
algorithm
Obstruction-free
algorithm
Sequential locking
Obstruction-free locking
DISC 2007
Gadi Taubenfeld © Sept. 2007

22. Our Transformation P1 P2 Obstruction-free algorithm Entry
Back to the lock-free model P1 P2
The winner increment a counter C
every X steps of the OF algorithm.
A loser, p, delays itself for C time units.
Obstruction-free
algorithm
if C was updated p delays again,
otherwise, p releases the lock.
Entry
Critical Section
Exit
Problems:
1. the winner may be alive;
2. two processes hold the lock;
3. p may release the lock at some
unexpected time later on.
Obstruction-free
algorithm
DISC 2007
Gadi Taubenfeld © Sept. 2007

23. Our Transformation P1 P2 Obstruction-free algorithm Entry
Solution -- not so simple … P1 P2
The winner tries to acquire the lock
again. But, before doing so, it has to
wait long enough so that other processes
that have mistakenly concluded that it
has crashed will have enough time
to release the lock again …
Obstruction-free
algorithm
Entry
Critical Section
Exit
Problems:
1. the winner may be alive;
2. two processes hold the lock;
3. p may release the lock at some
unexpected time later on.
Obstruction-free
algorithm
DISC 2007
Gadi Taubenfeld © Sept. 2007

24. The End
DISC 2007
Gadi Taubenfeld © Sept. 2007