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Improving the Performance Competitive Ratios of Transactional Memory Contention ManagersPowerPoint Presentation

Improving the Performance Competitive Ratios of Transactional Memory Contention Managers

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### Improving the Performance Competitive Ratios of Transactional Memory Contention Managers

Gokarna Sharma

Costas Busch

Louisiana State University, USA

WTTM 2010 - 2nd Workshop on the Theory of Transactional Memory

STM Systems Transactional Memory Contention Managers

- Progressis ensured through contention management (CM) policy
- Performance is generally evaluated by competitive ratio
- Makespan primarily depends on the TM workload
- arrival times, execution time durations, release times, read/write sets

- Challenge
- How to schedule transactions such that it reduces the makespan?

WTTM 2010 - 2nd Workshop on the Theory of Transactional Memory

Related Work Transactional Memory Contention Managers

- Mostly empirical evaluation
- Theoretical Analysis
- [Guerraoui et al., PODC’05]
- GreedyContention Manager, Competitive Ratio = O(s2) (sis the number of shared resources)

- [Attiya et al., PODC’06]
- Improved the competitive ratio of Greedy to O(s)

- [Schneider & Wattenhofer, ISAAC’09]
- RandomizedRounds Contention Manager, Competitive Ratio = O(C logn) (C is the maximum number of conflicting transactions and n is the number of transactions)

- [Attiya & Milani, OPODIS’09]
- Bimodal scheduler, Competitive Ratio = O(s) (for bimodal workload with equi-length transactions)

- [Guerraoui et al., PODC’05]

WTTM 2010 - 2nd Workshop on the Theory of Transactional Memory

Our C Transactional Memory Contention Managersontributions

- Balanced TM workloads
- Two polynomial time contention management algorithms that achieve competitive ratio very close to O() in balanced workloads
- Clairvoyant – Competitive ratio = O()
- Non-Clairvoyant – Competitive ratio = O(logn) w.h.p.

- Lower bound for transaction scheduling problem

WTTM 2010 - 2nd Workshop on the Theory of Transactional Memory

Roadmap Transactional Memory Contention Managers

- Balanced workloads
- CM algorithms and proof intuitions
- Lower bound and proof intuition

WTTM 2010 - 2nd Workshop on the Theory of Transactional Memory

Balanced Workloads Transactional Memory Contention Managers

- A transaction is balanced if:
- ≤ , ≤ ≤ 1 is some constant called balancing ratio
- and are number of writes and reads to shared resources by , respectively

- For read-onlytransaction, = 0, and for write-onlytransaction, = 0
- A workload is balanced if:
- It contains only balanced transactions

WTTM 2010 - 2nd Workshop on the Theory of Transactional Memory

Algorithms Transactional Memory Contention Managers

- Clairvoyant
- Clairvoyant in the sense it requiresknowledge of dynamic conflict graph to resolve conflicts
- Competitive ratio = O()

- Non-Clairvoyant
- Non-Clairvoyant in the sense it doesnot require knowledge of conflict graph to resolve conflicts
- Competitive ratio = O(logn)with high probability
- Competitive ratio O(logn) factor worse than Clairvoyant

WTTM 2010 - 2nd Workshop on the Theory of Transactional Memory

Proof Transactional Memory Contention ManagersIntuition (1/2)

- Knowing ahead the execution times ()and total number of shared resource accesses (|R(Ti)|)of transactions
- Intuition
- Divide transactions into +1groups according to execution time, where=
- Again divide each group into subgroups according to shared resource accesses needed, where =
- Assign a total order among the groups and subgroups

WTTM 2010 - 2nd Workshop on the Theory of Transactional Memory

Proof Intuition Transactional Memory Contention Managers(2/2)

- Analysis
- For a subgroup Aij, competitive ratio = O(min(, )), where = 2j+1 -1
- For a group Ai, competitive ratio = O() after combining competitive ratios of all the subgroups
- After combining competitive ratios of all groups, competitive ratio = O(
- For = O(1) and = O(1), competitive ratio = O()

- O(logn) factorin Non-Clairvoyant due to the use of random priorities to resolve conflicts

WTTM 2010 - 2nd Workshop on the Theory of Transactional Memory

Lower Transactional Memory Contention ManagersBound (1/2)

- We prove the following theorem
- Unless NP ZPP, we cannot obtain a polynomial time transaction scheduling algorithm such that for every input instance with = 1 and = 1 of the TRANSACTION SCHEDULING problem the algorithm achieves competitive ratio smaller than O(()1-) for any constant > 0.

- Proof Intuition
- Reduce the NP-Complete graph coloring problem, VERTEX COLORING, to the transaction scheduling problem, TRANSACTION SCHEDULING
- Use following result [Feige & Kilian, CCC’96]
- No better than O(n(1- )) approximation exists for VERTEX COLORING, for any constant >0, unless NP ZPP

WTTM 2010 - 2nd Workshop on the Theory of Transactional Memory

Lower Bound Transactional Memory Contention Managers(2/2)

- Reduction: Considerinput graph G = (V, E) of VERTEX COLORING, where |V| = n and |E|= s
- Constructa set of transactions Tsuch that
- For each v ϵV, there is a respective transaction TvϵT
- For each e ϵE, there is a respective resource ReϵR

- Let G’ be the conflict graph for the set of transactions T
- G’ is isomorphic to G, for = 1, min= max = 1, and = 1
- Valid k-coloring in G implies makespan of step k in G’ for T

- Algorithm Clairvoyant is tight for = O(1) and = O(1)

WTTM 2010 - 2nd Workshop on the Theory of Transactional Memory

Conclusions Transactional Memory Contention Managers

- Balanced TM workloads
- Two new randomized CM algorithms that exhibit competitive ratio very close to O()in balanced workloads
- Lower bound of O()for transaction scheduling problem

WTTM 2010 - 2nd Workshop on the Theory of Transactional Memory

[Full paper to appear in OPODIS 2010] Transactional Memory Contention Managers

arXiv version: http://arxiv.org/abs/1009.0056v1.pdf

Thank You!!!

WTTM 2010 - 2nd Workshop on the Theory of Transactional Memory

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