Improving the performance competitive ratios of transactional memory contention managers
Download
1 / 13

Improving the Performance Competitive Ratios of Transactional Memory Contention Managers - PowerPoint PPT Presentation


  • 68 Views
  • Uploaded on

Improving the Performance Competitive Ratios of Transactional Memory Contention Managers. Gokarna Sharma Costas Busch Louisiana State University, USA. STM Systems. Progress is ensured through contention management (CM) policy Performance is generally evaluated by competitive ratio

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Improving the Performance Competitive Ratios of Transactional Memory Contention Managers' - estrella-gomez


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Improving the performance competitive ratios of transactional memory contention managers

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
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
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)

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


Our c ontributions
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
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
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
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 intuition 1 2
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 2 2
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 bound 1 2
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 2 2
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
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


Improving the performance competitive ratios of transactional memory contention managers

[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