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TOWARDS SCALABILITY IN TUPLE SPACES. Philipp Obreiter, Guntram Gräf Telecooperation Office (TecO) University of Karlsruhe. Scalability. Five dimensions: size of tuples number of tuples in the tuple space number of considered tuple spaces throughput of the tuple space number of clients.

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Towards scalability in tuple spaces

TOWARDS SCALABILITYIN TUPLE SPACES

Philipp Obreiter, Guntram Gräf

Telecooperation Office (TecO)

University of Karlsruhe


Scalability

Obreiter/Gräf: Towards Scalability in Tuple Spaces

Scalability

Five dimensions:

  • size of tuples

  • number of tuples in the tuple space

  • number of considered tuple spaces

  • throughput of the tuple space

  • number of clients


Goals

Obreiter/Gräf: Towards Scalability in Tuple Spaces

Goals

Scalable tuple space

  • without schematic restrictions

    Procedure:

  • formalize and classify tuples

  • analyze former indexing strategies

  • deduce a new indexing strategy

  • conceive the architecture and implementation of a scalable tuple space


  • Hierarchy of fields f match f

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    Hierarchy of fields (F,matchF)

    F

    int

    string

    1234

    5678

    “Hello“

    “World“


    Hierarchy of fields

    F

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    x modulo y

    fraction

    x modulo 3

    x modulo 5

    1/2

    6/9

    2/4

    4/6

    0

    1

    0

    1

    2

    4

    2

    3

    Hierarchy of fields


    Hierarchy of tuples match

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    

    (int,F)

    (F, string)

    (int,(int,int))

    (int,string)

    (F,“Hello“)

    (1234,(56,78))

    (int,“Hello“)

    (1234,string)

    (5678,“Hello“)

    Hierarchy of tuples (,match)


    Distribution model

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    Distribution model

    • Set of p servers {1,...,p}

    • Distribution (W,R) for tuple t

      • writes to W(t) {1,...,p}

      • reads fromR(t) {1,...,p}

    • condition for correctness

      match(t1,t2) W(t2)  R(t1)  

    1

    2

    3

    4

    5

    6

    R

    W


    Conceiving a distribution

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    Conceiving a distribution

    W(t)

    t

    t

    Abstract representation

    • uncouples abstraction of tuples and adjustment to p

    • is an efficient data structure

    W(t)

    abstract

    representation

    R(t)

    R(t)

    directly

    indirectly


    Indexing based on hashing i

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    (F)

    (printer,F,F)

    (F,1200dpi,F)

    (scanner,F,F)

    (printer,1200dpi,F)

    (scanner,1200dpi,F)

    (F,1200dpi,x.x.x.x)

    P1

    S4

    P3

    S3

    P2

    P4

    P5

    S1

    S2

    S5

    Indexing based on hashing (I)


    Indexing based on hashing ii

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    (F)

    (printer,F,F)

    (F,1200dpi,F)

    (scanner,F,F)

    (printer,1200dpi,F)

    (scanner,1200dpi,F)

    (F,1200dpi,x.x.x.x)

    P1

    S4

    P3

    S3

    P2

    P4

    P5

    S1

    S2

    S5

    Indexing based on hashing (II)

    {1}

    {7}

    {2}

    {6}

    {12}

    {8}

    {5}

    {8}

    {3}

    {5}


    Indexing based on hashing iii

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    (F)

    (printer,F,F)

    (F,1200dpi,F)

    (scanner,F,F)

    (printer,1200dpi,F)

    (scanner,1200dpi,F)

    (F,1200dpi,x.x.x.x)

    P1

    S4

    P3

    S3

    P2

    P4

    P5

    S1

    S2

    S5

    Indexing based on hashing (III)

    {7}

    {3}


    Indexing based on hypercubes

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    Indexing based on hypercubes

    • Fields:

      • hierarchical structure intervals instead of points

      • correctness: matchF(f1,f2)  F(f2)  F(f1)

    • Tuples:

      • tuple complex  multi-dimensional index

      • induces transformation  to hypercubes

    • Distribution:

      • Partition hyperspace into tuple domains1,... p

      • (,) permissible with (t):= {q | q(t)   }


    Disjoint complete tuple domains

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    disjoint/complete tuple domains

    x1

    5

    T6

    4

    T4

    3

    T5

    2

    T3

    1

    T1

    T2

    x2

    -1

    0

    1

    2

    3

    4

    5


    Disjoint complete tuple domains1

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    disjoint/complete tuple domains

    x1

    1

    2

    5

    T6

    4

    T4

    3

    3

    T5

    2

    4

    5

    T3

    1

    T1

    T2

    x2

    -1

    0

    1

    2

    3

    4

    5


    Tree of tuple domains

    x2 = 0

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    x1 = 2

    2

    x1 = 4

    x2 = 3

    4

    5

    3

    2

    Tree of tuple domains


    Overlapping incomplete tuple domains

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    Overlapping/incomplete tuple domains

    x1

    2

    5

    T6

    1

    4

    T4

    3

    3

    T5

    2

    T3

    1

    T1

    T2

    x2

    -1

    0

    1

    2

    3

    4

    5


    S a t u s

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    SATUS

    • Implementation of a Scalable Tuple Spaces

    • Management interface

    • Extension to four tiers

    • Built-in standard fields

    • Validated with respect to:

      • Efficiency of the distribution

      • Efficiency of adaptive tuple domains


    Efficiency of the distribution

    Rate

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    Efficiency of the distribution

    1

    .8

    pruning rate

    .6

    .4

    .2

    overhead

    n

    0

    50

    100

    150

    200

    250

    300

    350

    400

    450

    500


    Questions

    Obreiter/Gräf: Towards Scalability in Tuple Spaces

    Questions?


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