Competitive Freshness Algorithms for Wait-free Data Objects

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Competitive Freshness Algorithms for Wait-free
Data Objects

• Peter Damaschke, Phuong Ha Philippas Tsigas

Presentation at the Euro-Par 2006 29th Aug. 1st
Sept. 2006, Dresden, Germany.
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Wait-free data objects
Introduction Modeling the problem Deterministic
algorithm Randomized algorithm Conclusions

• Concurrent data objects
• Consistency!
• Solutions
• Mutual exclusion?
• ? risks of lock-convoy, deadlock priority
  inversion ?
• Non-blocking synchronization
• Wait-free
• every operation is guaranteed to finish in a
  limited number of steps.
• ? Suitable for real-time systems

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Freshness
Introduction Modeling the problem Deterministic
algorithm Randomized algorithm Conclusions

• Reactive systems need read-operations that both
  respond fast and return fresh values

e0d
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Earlier work
Introduction Modeling the problem Deterministic
algorithm Randomized algorithm Conclusions

• Freshness in databases
• Freshness in caching systems
• Freshness for concurrent data objects
• single-writer-to-single-reader asynch. comm.

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Contributions
Introduction Modeling the problem Deterministic
algorithm Randomized algorithm Conclusions

• The first paper that attacks the freshness for
  multi-writer multi-reader shared objects
• Competitive freshness
• An optimal deterministic algorithm
• A competitive randomized algorithm

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Road-map
Introduction Modeling the problem Deterministic
algorithm Randomized algorithm Conclusions

• Introduction
• Modeling the problem
• Optimal deterministic algorithm
• Nearly-optimal randomized algorithm
• Conclusions

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Model
Introduction Modeling the problem Deterministic
algorithm Randomized algorithm Conclusions

• Assumptions
• An upper bound D on operation execution time
• Freshness
• Constraints

and
d delay, 1 ? d ? D1 ed fresh values M
concurrent writes at e0
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Freshness as an online game
Introduction Modeling the problem Deterministic
algorithm Randomized algorithm Conclusions
freshness (log)
lnD

• Online game
• player (read operation)
• vs.
• malicious adversary

X
time (log)
0
lnD
Freshness
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A deterministic algorithm
Introduction Modeling the problem Deterministic
algorithm Randomized algorithm Conclusions
Algorithm The read accepts the first
Analysis
fT
fT - ?
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Lower bound
Introduction Modeling the problem Deterministic
algorithm Randomized algorithm Conclusions

• Adversarys strategy
• Start with cln(D)/2 decrease c at unit speed
  until the player stops. At this time,
• if c gt 0, c jumps to the max.
• if c ? 0, c keeps decreasing
• Case 1
• f1 - p1 ln D / 2
• Case 2
• f2 - p2 ln D / 2
• ? Comp. ratio e(f-p)

f
lnD
f1
f2
p1
lnD
0
t
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A randomized algorithm
Introduction Modeling the problem Deterministic
algorithm Randomized algorithm Conclusions

• Ideas
• Put a probability on the freshness c when it
  starts to go down.
• Algorithm
• When c is decreasing, put on it a probability
• If the game is over (i.e. hg), put the rest r on
  the current c

f
lnD
g
h
a
c
0
lnD
t
t1
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A randomized algorithm
Introduction Modeling the problem Deterministic
algorithm Randomized algorithm Conclusions

• Competitive ratio
• Optimal randomized comp. ratio (ln D)/2,
  asymptotically
• (cf. TR-CS-200517)

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Conclusions
Introduction Modeling the problem Deterministic
algorithm Randomized algorithm Conclusions

• The first paper that defines the freshness
  problem for wait-free data objects.
• Competitive freshness
• An optimal deterministic algorithm
• A nearly-optimal randomized algorithm
• Contributions to the online search problem
• New general models

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Thank you for your attention!