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Locality in Concurrent
Data Structures
Hagit Attiya
Technion
Abstract Data Types (ADT)

Abstract representation of data
& set of methods (operations)
for accessing it
data
– Signature
– Specification
May 13, 2008
Locality @ BGU
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Implementing High-Level ADT
From lower-level ADTs
High-level operations translate into
primitives on base objects
– Obvious: read, write
– Common: compare&swap (CAS),
LL/SC,
– Double-CAS (DCAS),
– Generic: read-modify-write (RMW),
kRMW, kCAS, …
Low-level operations can be
implemented from more primitive
operations
– A hierarchy of implementations
May 13, 2008
Locality @ BGU
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Example: Binary Operations
Atomically read and modify two memory locations (esp. DCAS)
 Simplify the writing of concurrent ADTs
 kCAS is even better
Virtual Locking: Simulate DCAS / kCAS with a single-item CAS
– Acquire virtual locks on nodes in the data set

Perhaps in some order
– Handle conflicts with blocking operations (holding a
required data item)
May 13, 2008
Locality @ BGU
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Virtual locking
[Turek, Shasha, Prakash, 1992] [Barnes]

Acquire locks by increasing addresses
– Guarantees that the implementation is nonblocking


Help the blocking operation to complete
(recursively)
May result in long helping chains
May 13, 2008
Locality @ BGU
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Virtual Locking: Reducing Contention
[Shavit, Touitou, 1995]




Release locks when the operation is blocked
Help an immediate neighbor (only) & retry…
Short helping chains
But long delay chains
May 13, 2008
Locality @ BGU
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Randomization: How Often this Happens?
[Ha, Tsigas, Wattenhofer, Wattenhofer, 2005]


Operations choose locking order at random
Chains’ length depends on log n / loglog n
– Also experimentally
– Better, and yet…

Similar analysis for chains’ length when ops choose
items at random
– Depends on the operations’ density
[Dragojevic, Guerraoui & Kapalka, 2008]
May 13, 2008
Locality @ BGU
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Color-Based Virtual Locking (Binary)
[Attiya, Dagan, 1996]


Operations on two data items (e.g., DCAS)
Colors define the locking order
– Inspired by the left-right dinning philosophers algorithm
[Lynch, 1980]


Color the items when the operation starts
– Non-trivial…
Bound the length of delay chains
– But the coloring stage is complicated
[Cole, Vishkin, 1986]
<
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Locality @ BGU
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Color-Based Virtual Locking (Fixed k)
[Afek, Merritt, Taubenfeld, Touitou, 1997]


Implements operations on k items, for a fixed k
Based on the memory addresses, the conflict graph
is decomposed into trees & items are legally colored
[Goldberg, Plotkin, Shannon]
– Need to have the data set from the beginning
– Recursive, with A&D at the basis and in each step
– Even more complicated
May 13, 2008
Locality @ BGU
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Virtual Locking: More Concurrency, Simpler
[Attiya, Hillel, 2008]

Acquire locks in arbitrary order
– No need to know the data set
(or its size) in advance
– No pre-computation
Possible ways to handle conflicts between
operations contending for a data item
– Wait for the other operation
– Help the other operation
– Reset the other operation
May 13, 2008
Locality @ BGU
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Conflict Resolution, How?
Depends on the operations’ progress
More advanced operation wins
1. How to gauge progress?
2. What to do on a tie?
May 13, 2008
Locality @ BGU
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Who’s More Advanced?


The operation that locked
more data items
If a less advanced operation
needs an item
 help the conflicting operation or
 wait (blocking in a limited radius)

If a more advanced operation
needs an item
 reset the conflicting operation
and claim the item
May 13, 2008
Locality @ BGU
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What about Ties?
2
2
Happen when two transactions
locked the same number of items
A transaction has a descriptor
and a lock
Use DCAS to race for locking the
two descriptors
– Winner calls the shots…
May 13, 2008
Locality @ BGU
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Measuring Concurrency:
Data Items and Operations
A data structure is a collection of
items
An operation accesses a data set
– not necessarily a pair
A set of operations induces a
conflict graph
– Nodes represent items
– Edges connect items of the same
operation
May 13, 2008
Locality @ BGU
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Spatial Relations between Operations
Disjoint access
– Non adjacent edges
– Distance is infinite
Overlapping operations
– Adjacent edges
– Distance is 0
Chains of operations
– Paths
– Distance is length of path (here, 2)
d-neighborhood of an operation:
all operations at distance ≤ d
May 13, 2008
Locality @ BGU
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Interference between Operations
Disjoint access
Overlapping operations
Non-overlapping operations
Provides more concurrency &
yields better throughput
May 13, 2008
Locality @ BGU
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Measuring Concurrency: Locality
d failure locality [Choi, Singh, 1992]
some operation completes in
the d-neighborhood
unless a failure occurs
in the d-neighborhood
d-local nonblocking
some operation completes in
the d-neighborhood
even if a failure occurs
in the d-neighborhood
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Locality @ BGU
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Quantitative Measures of Locality
[Afek, Merritt, Taubenfeld, Touitou, 1997]
Distance in the conflict graph between
overlapping operations that interfere
d-local step complexity:
Only operations at distance ≤ d
delay each other
d-local contention:
Only operations at distance ≤ d
access the same memory location
May 13, 2008
Locality @ BGU
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In Retrospect
Algorithm
Step locality Memory
locality
Turek et al.
O(n)
O(n)
Shavit,
Touitou
O(n)
O(1)
Comments
Attiya, Dagan O(log*n)
O(log*n)
Binary
Afek et al.
O(k+log*n)
O(k+log*n)
Fixed k
Attiya, Hillel
O(k+log*n)
O(k+log*n)
Flexible k
May 13, 2008
Locality @ BGU
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Customized Virtual Locking



Can be viewed as software transactional memory
– High overhead
Or handled by specialized algorithms
– Ad-hoc and very delicate, mistakes happen
Instead, design algorithms in a systematic manner…
 Lock the items that have to be changed &
apply a sequential implementation on these items
 Lock items by colors to increase concurrency
 No need to re-color at the start of each operations since with a
specific data structure
 We manage a data structure since its infancy
 The data sets of operations are predictable
May 13, 2008
Locality @ BGU
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Example: Doubly-Linked Lists


An important special case underlying many distributed data
structures
– E.g., priority queue is used as job queue
Insert and Remove operations
– Sometimes only at the ends (deques)
– The data set is an item and its left / right neighbors (or left / right
anchor)
May 13, 2008
Locality @ BGU
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Built-In Coloring for Doubly-Linked Lists


An important special case underlying many distributed data
structures
– E.g., priority queue is used as job queue
Insert and Remove operations
– Sometimes only at the ends (deques)
– The data set is an item and its left / right neighbors (or left / right
anchor)
[Attiya, Hillel, 2006]
 Always maintain the list items legally colored
– Adjacent items have different colors
– Adjust colors when inserting or removing items
– No need to color from scratch in each operation!
 Constant locality: operations that access disjoint data sets do not
delay each other
May 13, 2008
Locality @ BGU
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Insert Operation

New items are assigned a temporary color

Remove from the ends is similar to Insert
– Locks three items, one of them an anchor
new
item
<
May 13, 2008
Locality @ BGU
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<
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Removing from the Middle

Complicated: Need to lock three list items
– Possibly two with same color

A chain of Remove operations may lead to a long
delay chain in a symmetric situation
May 13, 2008
Locality @ BGU
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To the Rescue: DCAS Again
 Use DCAS to lock equally colored nodes
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Locality @ BGU
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In Treatment

DCAS???
– Supported in hardware, or at least
with hardware transactional memory
– Software implementation (e.g., A&D)

Software transactional memory?!
– Speculative execution
– Read accesses

Blocking?!!!
– Not so bad w/ low failure locality
– Can be translated to nonblocking locality
May 13, 2008
Locality @ BGU
26
Randomization: How Often this Happens?
[Ha, Tsigas, Wattenhofer, Wattenhofer, 2005]


Operations choose locking order at random
Chains’ length depends
on log n / loglog n
– better, and yet…

Similar analysis for chains’ length when ops choose
items at random
– Depends on the operations’ density
[Dragojevic, Guerraoui & Kapalka, 2008]
May 13, 2008
Locality @ BGU
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