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DICE: Distributed Interactive Cube Exploration

DICE: Distributed Interactive Cube Exploration

Arnab Nandi

March 31, 2014
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  1. DICE: Distributed and 

    Interactive Cube Exploration


    Niranjan Kamat

    Prasanth Jayachandran*

    Karthik Tunga*

    Arnab Nandi

    *Work done while at Ohio State 0

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  2. Overview
    •  Large-scale ad-hoc analytics: Think of the User!
    •  Query Sessions
    •  Interactive response times
    •  DICE: Distributed Interactive Cube Exploration
    •  Speculation
    •  Faceted Model
    •  Online Sampling
    •  Interactive Performance
    •  Synthetic & Real-World Workloads
    •  User Studies
    1

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  3. Motivation
    •  Data Cube Materialization is Expensive
    •  Large datasets (scale: billion tuples)

    •  Ad-hoc Cube Exploration
    •  Distributed Aggregation (scale: 10-100 nodes)
    •  Interactive Response Times (scale: seconds)
    •  Fluid data exploration experience
    2

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  4. Why Interactive?
    •  Query Sessions
    •  Iterate faster
    •  Human-in-the-loop
    •  Improve understanding
    3

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  5. Outline
    •  Motivation
    •  Preliminaries
    •  DICE Concepts
    •  Speculative Execution
    •  Faceted Traversals
    •  Sampling
    •  Implementation
    •  Experiments
    5

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  6. Preliminaries: Data Cube
    SELECT COUNT(uid)
    FROM user.table as
    (uid, color, gender)
    CUBE ON color, gender
    •  Aggregate based on all
    possible combinations of
    dimensions
    •  Measure = COUNT
    •  Dimensions = color, gender
    6

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  7. Preliminaries: Data Cube
    <"*,"*">"
    <"*,"gender>" <"color,"*">"
    "
    Men$ Women$ Total$
    Red$ 3" 1" 4"
    Green$ 1" 2" 3"
    Total$ 4" 3" 7"
    ! 
    Cube"La8ce"
    7

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  8. Preliminaries: Data Cube
    Men$ Women$ Total$
    Red$ 3" 1" 4"
    Green$ 1" 2" 3"
    Total$ 4" 3" 7"
    8
    Apple"
    Apple"
    Mango"
    Mango"
    Mango"
    Mango"
    (apple)$ Men$ Women$ Total$
    Red$ 1" 1" 2"
    Green$ 1" 0" 1"
    Total$ 2" 1" 3"
    (mango)$ Men$ Women$ Total$
    Red$ 2" 0" 2"
    Green$ 0" 2" 2"
    Total$ 2" 2" 4"
    Apple"
    ! 
    New
    dimension

    = fruit

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  9. *$ Men$ Women$ *$
    Red$ 3" 1" 4"
    Green$ 1" 2" 3"
    Total$ 4" 3"
    (mango)$ Men$ Women$ *$
    Red$ 2" 0" 2"
    Green$ 0" 2" 2"
    Total$ 2" 2"
    Preliminaries: Data Cube
    (apple)$ Men$ Women$ *$
    Red$ 1" 1" 2"
    Green$ 1" 0" 1"
    *$ 2" 1" 3"
    gender"
    color"
    9
    Apple"
    Apple"Apple"
    Mango"
    Mango"
    Mango"
    Mango"

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  10. <"*,"*">"
    <"*,"gender>" <"color,"*">"
    "
    Cube Materialization is Expensive
    <*, *, *>
    <*, iops, *> <*, *, zone>
    <*, iops, zone> <*, *, datacenter>
    <*, iops, datacenter> <*, *, rack>
    <*, iops, rack>



    Figure 2: Lattice for the hierarchical attributes
    ticu
    gro
    exp
    Thi
    chi
    cha
    the
    effe
    or a
    piv
    ses
    as f
    Fac
    g 2
    me
    10

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  11. Cube Exploration
    <*, *, *>
    <*, iops, *> <*, *, zone>
    <*, iops, zone> <*, *, datacenter>
    <*, iops, datacenter> <*, *, rack>
    <*, iops, rack>



    Figure 2: Lattice for the hierarchical attributes
    ticu
    gro
    exp
    Thi
    chi
    cha
    the
    effe
    or a
    piv
    ses
    as f
    Fac
    g 2
    me
    11

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  12. Outline
    •  Motivation
    •  Preliminaries
    •  DICE Concepts
    •  Speculative Execution
    •  Faceted Traversals
    •  Sampling
    •  Implementation
    •  Experiments
    12

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  13. The DICE System
    •  Distributed Aggregation (scale: 10-100 nodes)
    •  Large datasets (scale: billion tuples)
    •  Interactive Response Times (scale: seconds)
    13

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  14. Concept: Faceted Exploration
    •  Challenge: A single data cube has an
    exponential number of queries
    •  Which one to pick?
    •  Restricts Cube Exploration
    •  Lesser options = We can predict what the
    user is querying next better
    16

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  15. Faceted Example: Parent
    •  SELECT rack, AVG(iops) 

    FROM events 

    WHERE 

    ! ! ! !datacenter = "EU" 

    " "AND "hour = 6 

    GROUP BY rack; "
    17
    •  SELECT rack, AVG(iops) 

    FROM events 

    WHERE 

    ! ! ! !datacenter = * 

    " "AND "hour = 6 

    GROUP BY rack; "
    a,b"
    b"
    a"
    Parent"
    "
    *"

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  16. Faceted Example: Child
    •  SELECT rack, AVG(iops) 

    FROM events 

    WHERE 

    " " " "datacenter = "EU" 

    " "AND "hour = 6 

    GROUP BY rack; "
    18
    •  SELECT rack, AVG(iops) 

    FROM events 

    WHERE 

    ! ! ! !rack = 25

    " "AND "hour = 6 

    GROUP BY rack; "
    Child"
    a,b"
    b"
    a"
    *"

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  17. Faceted Example: Sibling
    •  SELECT rack, AVG(iops) 

    FROM events 

    WHERE 

    ! ! ! !datacenter = "EU" 

    " "AND "hour = 6 

    GROUP BY rack; "
    19
    •  SELECT rack, AVG(iops) 

    FROM events 

    WHERE 

    " " " "datacenter = “US” 

    " "AND "hour = 6 

    GROUP BY rack; "
    a,b"
    b"
    a"
    *"
    Sibling"

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  18. Faceted Example: Pivot
    •  SELECT rack, AVG(iops) 

    FROM events 

    WHERE 

    ! ! ! !datacenter = "EU" 

    " "AND "hour = 6 

    GROUP BY rack; "
    20
    •  SELECT rack, AVG(iops) 

    FROM events 

    WHERE 

    " " " "rack = “12” 

    " "AND "hour = 6 

    GROUP BY datacenter; !
    a,b"
    b"
    a"
    *"
    Pivot"

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  19. Faceted Traversal
    •  Intuitive Exploration
    •  Can cover entire cube lattice
    •  Limits number of speculated queries
    21

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  20. Outline
    •  Motivation
    •  Preliminaries
    •  DICE Concepts
    •  Speculative Execution
    •  Faceted Traversals
    •  Sampling
    •  Implementation
    •  Experiments
    22

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  21. Concept: Sampling
    •  Tradeoff: Accuracy vs. Response Time
    •  Run queries over a sample of the data if
    needed
    •  How do we accurately provide estimates from
    sampled data?
    •  What sampling rate should we use?

    23

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  22. Concept : Sampling
    •  Provide confidence intervals for all
    estimates using variance across samples
    ugging in the values from above into Equation 1, we would get
    e variance for the combined group [rack:1,hour:6,datacenter:EU]
    s2
    1
    = 8.32 and for [rack:2,hour:6,datacenter:EU] as s2
    2
    = 11.52
    The standard deviation can be used as an error estimate for the
    tire query. Once we know the variance of each of the combined
    oups, we can get an error estimate for the combination of all of
    ese groups i.e. the combined result set. We consider three mea-
    res SUM, AVG and COUNT. The variance of the estimator for the
    easure SUM can be given as:
    ˆ
    V [ˆ
    t] =
    H
    X
    h=1
    N2
    h
    (1
    nh
    Nh
    )
    ˆ
    sh
    2
    nh
    (2)
    milarly, variance of the estimator for the measure AVG:
    ˆ
    V [ˆ
    y] =
    H
    X
    h=1
    N2
    h
    N2
    (1
    nh
    Nh
    )
    ˆ
    sh
    2
    nh
    (3)
    Thus, a facet fx(dxg,
    !
    dxb : vxb) can be pivoted to the facet
    fy(dyg,
    !
    dyb : vyb) if dyg 2
    !
    dxb ^ dxg 2
    !
    dyb and !
    vxb and !
    vyb have
    all but one bound dimension (and value) in common. The facet
    (zone)[week:w1
    , iops:i1] pivots on iops i1
    from the facet exam-
    ple, and is therefore its pivot facet.
    Explorability of the cube: It is critical that the user be able to
    fully explore the data cube, i.e. all cube groups can be explored us-
    ing facets, and it is possible to reach any facet from any other facet.
    First, for a group g =
    !
    d : v, there can be |
    !
    d | facets, f(dg,
    !
    db : vb) :
    dg 2
    !
    d ^
    !
    db =
    !
    d dg. Second, any two facets in a region can
    be reached from another by a series of sibling and pivot traversals:
    sibling traversals to change bound values, and pivot traversals to
    switch between bound and grouped dimensions. Parent and child
    traversals allow us to reach the corresponding parent and child re-
    gions in the cube lattice. Thus, the four traversals enable full ex-
    ploration of the cube lattice.
    2.2 Distributed Execution
    Table Shards: We use sharded tables to achieve distributed and
    sampled execution of queries. A sharded table is the atomic unit
    of data in our system, and contains a subset of the rows of a SQL
    table and the concatenation of all shards across nodes is equiva-
    lent to the entire dataset. Each single node may contain multiple
    shards. Updates are atomic to each shard, and each session makes
    the assumption that the list of shards and the shards themselves do
    not change. We elaborate more the execution of queries over table
    shards in Section 3.3
    2.3 Querying over Sampled Data
    Symbol Explanation
    s2
    h
    variance of group h
    nh number of tuples in group h
    nhi
    number of tuples belonging to group h from
    the ith query
    mhi mean of the group h from the ith query
    mh mean of the group h from all queries
    vhi variance of the group h from the ith query
    ˆ
    V [ˆ
    t]
    variance of the estimator for the measure
    SUM
    ˆ
    V [ˆ
    y]
    variance of the estimator for the measure
    AVG
    ˆ
    V [ˆ
    p]
    variance of the estimator for the measure
    COUNT
    H
    Total number of groups in the union of all the
    queries
    Nh
    Total number of tuples in the combined group
    h
    nh
    Number of tuples in the sample in the com-
    sampling and post-stratification and present a methodology for do-
    ing so.
    In order to deliver results at higher sampling rates, DICE runs
    the same query on multiple shards on multiple nodes. This results
    in the same cube group of the facet query being possibly obtained
    from the multiple table shards. Hence, the statistics for the same
    group from these multiple queries need to be combined together.
    While combining the AVG, SUM and COUNT are straight forward,
    the variances can be combined as shown in Appendix A as:
    s2
    h
    =
    1
    nh 1
    (
    numQ
    X
    i=1
    nhi(mhi mh)2) +
    X
    i
    (nhi 1)vhi) (1)
    where numQ is the number of queries that a facet query needs to
    be replicated to, to achieve the user specified sampling rate.
    Continuing our motivating example, the faceted representation
    of the query is (rack)[hour:6,datacenter:EU] with the measure and
    measure dimension being AVG(iops) . We append the COUNT and
    VARIANCE measures to the queries since we need them as de-
    scribed in Equation 1. Let this query be run on a single shard on a
    couple of nodes and resulting into a sampling rate of 10%, return-
    ing us groups and the corresponding measures from the two queries
    respectively as:
    {[rack:1,hour:6,datacenter:EU,AVG:10,COUNT:5,VAR:4],
    [rack:2,hour:6,datacenter:EU,AVG:12,COUNT:6,VAR:2]} &
    {[rack:1,hour:6,datacenter:EU,AVG:5,COUNT:8,VAR:1],
    [rack:2,hour:6,datacenter:EU,AVG:6,COUNT:7,VAR:2]}.
    Plugging in the values from above into Equation 1, we would get
    the variance for the combined group [rack:1,hour:6,datacenter:EU]
    as s2
    1
    = 8.32 and for [rack:2,hour:6,datacenter:EU] as s2
    2
    = 11.52
    The standard deviation can be used as an error estimate for the
    entire query. Once we know the variance of each of the combined
    groups, we can get an error estimate for the combination of all of
    these groups i.e. the combined result set. We consider three mea-
    sures SUM, AVG and COUNT. The variance of the estimator for the
    measure SUM can be given as:
    ˆ
    V [ˆ
    t] =
    H
    X
    h=1
    N2
    h
    (1
    nh
    Nh
    )
    ˆ
    sh
    2
    nh
    (2)
    Similarly, variance of the estimator for the measure AVG:
    ˆ
    V [ˆ
    y] =
    H
    X
    h=1
    N2
    h
    N2
    (1
    nh
    Nh
    )
    ˆ
    sh
    2
    nh
    (3)
    all but one bound dimension (and value) in common. The facet
    (zone)[week:w1
    , iops:i1] pivots on iops i1
    from the facet exam-
    ple, and is therefore its pivot facet.
    Explorability of the cube: It is critical that the user be able to
    fully explore the data cube, i.e. all cube groups can be explored us-
    ing facets, and it is possible to reach any facet from any other facet.
    First, for a group g =
    !
    d : v, there can be |
    !
    d | facets, f(dg,
    !
    db : vb) :
    dg 2
    !
    d ^
    !
    db =
    !
    d dg. Second, any two facets in a region can
    be reached from another by a series of sibling and pivot traversals:
    sibling traversals to change bound values, and pivot traversals to
    switch between bound and grouped dimensions. Parent and child
    traversals allow us to reach the corresponding parent and child re-
    gions in the cube lattice. Thus, the four traversals enable full ex-
    ploration of the cube lattice.
    2.2 Distributed Execution
    Table Shards: We use sharded tables to achieve distributed and
    sampled execution of queries. A sharded table is the atomic unit
    of data in our system, and contains a subset of the rows of a SQL
    table and the concatenation of all shards across nodes is equiva-
    lent to the entire dataset. Each single node may contain multiple
    shards. Updates are atomic to each shard, and each session makes
    the assumption that the list of shards and the shards themselves do
    not change. We elaborate more the execution of queries over table
    shards in Section 3.3
    2.3 Querying over Sampled Data
    Symbol Explanation
    s2
    h
    variance of group h
    nh number of tuples in group h
    nhi
    number of tuples belonging to group h from
    the ith query
    mhi mean of the group h from the ith query
    mh mean of the group h from all queries
    vhi variance of the group h from the ith query
    ˆ
    V [ˆ
    t]
    variance of the estimator for the measure
    SUM
    ˆ
    V [ˆ
    y]
    variance of the estimator for the measure
    AVG
    ˆ
    V [ˆ
    p]
    variance of the estimator for the measure
    COUNT
    H
    Total number of groups in the union of all the
    queries
    Nh
    Total number of tuples in the combined group
    h
    nh
    Number of tuples in the sample in the com-
    bined group h
    N Total number of tuples in the dataset
    p
    Proportion of tuples selected by the where
    clause
    Table 2: List of notations used in this subsection.
    As mentioned before, the interactive nature of our use case ne-
    cessitates the approximation of results by executing queries over a
    In order to deliver results at higher sampling rates, DICE runs
    the same query on multiple shards on multiple nodes. This results
    in the same cube group of the facet query being possibly obtained
    from the multiple table shards. Hence, the statistics for the same
    group from these multiple queries need to be combined together.
    While combining the AVG, SUM and COUNT are straight forward,
    the variances can be combined as shown in Appendix A as:
    s2
    h
    =
    1
    nh 1
    (
    numQ
    X
    i=1
    nhi(mhi mh)2) +
    X
    i
    (nhi 1)vhi) (1)
    where numQ is the number of queries that a facet query needs to
    be replicated to, to achieve the user specified sampling rate.
    Continuing our motivating example, the faceted representation
    of the query is (rack)[hour:6,datacenter:EU] with the measure and
    measure dimension being AVG(iops) . We append the COUNT and
    VARIANCE measures to the queries since we need them as de-
    scribed in Equation 1. Let this query be run on a single shard on a
    couple of nodes and resulting into a sampling rate of 10%, return-
    ing us groups and the corresponding measures from the two queries
    respectively as:
    {[rack:1,hour:6,datacenter:EU,AVG:10,COUNT:5,VAR:4],
    [rack:2,hour:6,datacenter:EU,AVG:12,COUNT:6,VAR:2]} &
    {[rack:1,hour:6,datacenter:EU,AVG:5,COUNT:8,VAR:1],
    [rack:2,hour:6,datacenter:EU,AVG:6,COUNT:7,VAR:2]}.
    Plugging in the values from above into Equation 1, we would get
    the variance for the combined group [rack:1,hour:6,datacenter:EU]
    as s2
    1
    = 8.32 and for [rack:2,hour:6,datacenter:EU] as s2
    2
    = 11.52
    The standard deviation can be used as an error estimate for the
    entire query. Once we know the variance of each of the combined
    groups, we can get an error estimate for the combination of all of
    these groups i.e. the combined result set. We consider three mea-
    sures SUM, AVG and COUNT. The variance of the estimator for the
    measure SUM can be given as:
    ˆ
    V [ˆ
    t] =
    H
    X
    h=1
    N2
    h
    (1
    nh
    Nh
    )
    ˆ
    sh
    2
    nh
    (2)
    Similarly, variance of the estimator for the measure AVG:
    ˆ
    V [ˆ
    y] =
    H
    X
    h=1
    N2
    h
    N2
    (1
    nh
    Nh
    )
    ˆ
    sh
    2
    nh
    (3)
    Continuing with our example, we estimate Nh
    N
    by nh
    n
    and nh
    Nh
    by the sampling rate since we cannot know Nh without sampling
    the entire data.
    Again plugging in the values we get, ˆ
    y = 6.92 ⇤ 13/26 +
    8.77 ⇤ 13/26 = 7.85 and ˆ
    V [ˆ
    t] = (13
    26
    )2 ⇤ (1 0.1) ⇤ (8.32/13 +
    11.52/13) = 0.35
    For the measure COUNT, we can use the proportion estimator
    since the where clause acts as the indicator function and thus the
    variance of the estimator for COUNT can be given as:
    24

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  23. Concept: Sampling
    •  Challenge:
    •  What sampling rate should we use?
    •  Solution:
    •  Run user query at the requested sampling rate
    •  Run different speculative queries at different
    sampling rates
    •  Goal: Increase likelihood of next user query being
    cached at highest sampling rate
    25

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  24. Concept: Sampling
    •  Prioritize likely queries that yield highest
    accuracy gain

    •  Estimated Accuracy Gain at the Sampling
    Rate Rcurrent
    :

    •  Goodness Score for Query q at Rcurrent

    ue v to
    ave an
    erion is
    )/|R2
    |
    ue v as
    e tuples
    For the
    mongst
    Join
    orming
    en sam-
    ratified
    lows:
    w(t) =
    bute A
    having
    the value h between the entire relations R1
    and R2
    will be equal
    to N
    h
    = m1(h) ⇤ m2(h). Therefore, to obtain a stratified random
    sample of the rate f, there needs to be n
    h
    = f ⇤ m1(h) ⇤ m2(h)
    number of samples having the value of h in the join column. This
    dictates that amongst the m1(h) tuples n
    h
    tuples need to be selected
    with replacement.
    Since, this is a plain extension of Motwani algorithm from simple
    random sample to stratified random sample, the second relation is
    assumed to be present as a whole and not sampled. For each tuple
    in the sample S1
    of R1
    , join it with one of the tuples in the second
    relation.
    What we want is that there needs to be f ⇤m1(h)⇤m2(h) tuples
    in the join having the value of h. That criterion is satisfied by the
    algorithm.
    The next criterion is that the probability of each tuple being
    present in the join should be the same. We are not discriminating
    against any tuples in either S1
    or from R2
    . Hence, the probabil-
    ity of any join tuple amongst m1(h) ⇤ m2(h) will be the same.
    Hence, what we obtain is indeed a stratified sample of the join by
    modification of the Motwani algorithm.
    Score(q,R
    current
    ) = Prob(q) ⇤ AccuracyGain(R
    current
    )
    4. EVALUATION
    4.1 Experimental Setup
    Environment
    where predicates is generalized,
    en becomes as follows:
    the groups in this case can be
    n and count of all the groups in
    versal
    l, consider the resultant query
    h = ”January”
    from the original query can be
    aversals
    hat one of the where predicate
    h = ”February”
    re predicates is exchanged with
    mple a pivot query that respects
    ble. However, if there were an
    ld have added a where predicate
    the current online sampling.
    1.4 Result Reuse up the Cube based on Sam-
    pling
    It is clear that the results from a more specialized region can be
    used to a more generalized region (removal of a where predicate or
    groupby clause), i.e. as we go up the cube. Hence, consider the case
    where the data has been sampled in a stratified sampling manner.
    We can compute different regions of the cube using different sets of
    samples. As we go up the cube, we can use the information situated
    in the tree with that node as a root to give much more information
    to the user without having to run the query asked on that region at a
    higher sampling rate.
    AccuracyGain(Rcurrent) = c⇤( 1
    p
    Rcurrent
    1
    p
    Rcurrent+1
    )
    26

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  25. Outline
    •  Motivation
    •  Preliminaries
    •  DICE Concepts
    •  Speculative Execution
    •  Faceted Traversals
    •  Sampling
    •  Implementation
    •  Experiments
    27

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  26. 28
    MASTER$
    "
    Query"Federator"
    BI"Tool/"UI"
    slave1$
    DB$
    slave3$
    DB$
    slaveN$
    DB$
    slave2$
    DB$
    Result"Cache"
    Workers"
    Network"
    User Query
    Speculative
    Queries
    Results
    User"Query
    Next"Query
    User"Query
    Speculative""
    Queries
    Results
    DICE System

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  27. DICE: Frontend
    •  One possible frontend for DICE
    •  Demonstrates interactive cubing
    •  Guides the user through cube exploration
    29

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  28. DICE: Frontend
    30

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  29. DICE: In Action
    31

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  30. Outline
    •  Motivation
    •  Preliminaries
    •  DICE Concepts
    •  Speculative Execution
    •  Faceted Traversals
    •  Sampling
    •  Implementation
    •  Experiments
    32

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  31. Experimental Setup
    •  Small Cluster
    •  Master: 1x Quad Core i5, 16GB RAM
    •  15 slave nodes: 1x Quad Core Xeon, 4GB RAM
    •  Default sample size: 200M tuples

    •  Cloud Cluster
    •  Amazon EC2
    •  1 master, 50 slave nodes: c1.xlarge type
    •  7GB Memory, 8 virtual cores
    33

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  32. 34
    Performance: Scale
    sub-second response
    time at one billion
    tuples
    significant speedup
    vs. NOSPEC

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  33. Performance: Sample Workload
    Query 1
    Query 2
    Query 3
    Query 4
    Query 5
    Query 6
    Query 7
    Query 8
    Query 9
    Query 10
    35
    lesser
    variance
    lower response times

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  34. Impact on User Experience
    •  Real User sessions
    •  10 users, 10 queries each
    •  Blind “taste test”
    •  Unanimous preference for DICE

    •  NoSpec (Naive system) vs DICE
    •  7 seconds faster per session (54s vs 47s)

    36

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  35. Faceted Model Efficacy
    •  Are facets a good way to model 

    cube exploration?
    •  Internet Advertising Company
    •  Hadoop / HIVE infrastructure
    •  Large-scale analytics
    •  46 query sessions, 116 queries
    •  Modeled 100% of the queries
    37

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  36. Limitations / Future Work
    •  Extra Speculative Queries
    •  Single-user Support
    •  Single GroupBy
    38

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  37. Conclusion
    •  Large-scale analytics: Think of the User!
    •  Query Sessions
    •  Sub-second response times
    •  DICE: Distributed Interactive Cube Exploration
    •  Speculation
    •  Faceted Model
    •  Online Sampling
    •  Interactive Performance
    •  Synthetic & Real-World Workloads
    •  User Studies
    39

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  38. Thank you!
    40
    http://go.osu.edu/diceproject

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