Best-Effort Top-k Query Processing Under Budgetary Constraints

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• Best-Effort Top-k Query Processing Under
  Budgetary Constraints

Michal Shmueli-Scheuer (IBM Haifa Research Lab
and UCI)
Yosi Mass, Haggai Roitman
Chen Li
Ralf Schenkel, Gerhard Weikum
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Motivating Example
Mediation Systems
Achieve high query throughput.
Top-k
Top-k
results
queries
Engine
Online Analytics (e.g. logs)
Achieve high query throughput.
Michal Shmueli-Scheuer
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Traditional top-k query

• Pre-computed lists over multiple attributes.
• Combine scores by some monotonic aggregation
  function.
• Two accesses modes
• sorted access (Cs)
• random access (Cr)
• Objective Compute k objects with highest scores.

Rm Rm
c 0.9
b 0.6
g 0.5
..
a 0.4
R2 R2
d 0.87
a 0.85
f 0.5
..
c 0.2
R1 R1
a 0.9
b 0.6
c 0.5
..
d 0.4
sorted
n
m
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NRA algorithm (Fagin et al.)
Top-2
R2 R2
d 0.87
a 0.85
f 0.5
. ..
c 0.2
R1 R1
a 0.9
b 0.6
c 0.5
..
d 0.4
Best score
Worst score
highi
a 0.9,1.77
d 0.87,1.77
f SUM
mink
candidates

mink gt best-score of candidates
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NRA algorithm (Fagin et al.)
Top-2
R2 R2
d 0.87
a 0.85
f 0.25
. ..
c 0.2
R1 R1
a 0.9
b 0.6
c 0.5
..
d 0.4
Best score
Worst score
a 1.75,1.75
d 0.87,1.47
highi
mink
candidates
b 0.6,1.45
mink gt best-score of candidates
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NRA algorithm (Fagin et al.)
Top-2
R2 R2
d 0.87
a 0.85
f 0.25
. ..
c 0.2
R1 R1
a 0.9
b 0.6
c 0.5
..
d 0.4
Best score
Worst score
a 1.75,1.75
d 0.87,1.37
highi
mink
candidates
b 0.6,0.85
c 0.5,0.75
f 0.25,0.75
mink gt best-score of candidates
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Top-k with Budget Constraints
Top-2
R2 R2
a 1.0
b 0.9
c 0.85
d 0.8
e 0.7
t 0.6
f 0.4
..
R1 R1
s 0.95
u 0.93
t 0.92
d 0.9
x 0.5
y 0.4
z 0.2

d 1.7
t 1.52
NRA 12Cs 12 precision 0.5
Given budget B, maximize result quality
Cs1, Cr 3 f SUM
TA 7Cs 7Cr 28 precision 0
Budget 10 ?
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Contributions

• Sorted Accesses
• Efficient Plan
• Solution with Adaptive a
• Sorted and Random Accesses
• Efficient Plan
• Solution with Adaptive a
• Experiments

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Results Under Limited Budget
Results for limited budget
K results for unlimited
budget
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Efficient Plan- Sorted Accesses

• Assume that we know the k results for unlimited
  budget (REXACT).

• Plan L1,4 L2,2

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Efficient Plan- Sorted Accesses

• Goal find plan t, such that

Plans for B5
Denoted as ROPT
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Sorted Accesses

• Observations

L1
L2
L3
O1, SL1
O1, SL2
O2, SL1
O2, SL2
O2, SL3
Prefer high scores
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Observations contd.
titlewar descriptionweapon
Prefer large score reductions
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Score Utilities
Score gain
Score reduction
y 3
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Optimization Problem

• Bi-objective optimization problem
• util(Li,x) a gain (1-a) reduction

• Heuristics
• Fair Heuristic
• Rank Heuristic

Where m is the number of lists
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Adaptive ?
gain
reduction
)?)
(1-?(
time
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Adaptive ?
top-k
o1 ws,bs
o2 ws,bs
d(o4) 0.8-0.60.2
o3 0.8,bs
candidates
hight1
o4 0.6,bs
hight2
o6 ws,bs
Theobald et al. VLDB04
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Adaptive ?
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Efficient Plan- Random Accesses

• Observations
• random accesses occur always after sorted
  accesses have been finished.

schedule 1 SARASA.
schedule 2 SASARA.
precision(schedule1) precision(schedule2)
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Observations- contd.

• Random accesses are only useful to objects in
  REXACT.

top-k
L2
o1 ws,bs
o2, SL2
Precision reduced
o5 ws,bs
o5, Not in REXACT
o2 ws,bs
o5, SL2
candidates
o4 ws,bs
o1, SL2
o5 ws,bs
Precision remains the same
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Random Accesses

• When to switch from SA to RA?

)?(
(1-?(
time
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Random Accesses

• Switch from Sorted to Random
• R (1- ?)S
• S total cost of sorted accesses.
• R total cost for random accesses.

• Which items to access ?

• maximize expected score.

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Experimental Data

• TREC Terabyte
• 25M webpages
• 50 queries with average length of 3 words.
• IMDB
• 375,000 movies
• 20 queries , each with 4 attributes Title,
  Genre, Actors, Description
• Synthetic data
• Zipf, lists 2,6, objects 10000,1000000
• Aggregate Function Sum

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Evaluation Methods

• percentage of optimal precision

Ropt
Rexact
Ralg
Ropt

• SME

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Results- Sorted Accesses
TREC, k100

• Less budget, more improvement

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Varied k
IMDB, B400

• Lower K, more improvement.

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Number of Lists
Zipf, K100, B4000

• More lists, more improvement.

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Results- Random Accesses
TREC, k100,Cr10
TREC, K100, Cr100
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Related Works

• Minimize budget for optimal results
• the algorithm computes the exact results with
  minimum cost. (Bast et al. VLDB06, Bruno et al.
  ICDE02, Chang et al. SIGMOD02)
• Dual problem.
• Anytime top-k
• The algorithm collects statistics during
  processing, which can be used to provide
  probabilistic guarantees at any time during
  processing. (Aray et al. VLDB07)
• Do not do any optimizations.
• Approximate top-k
• approximate results with probabilistic
  guarantees. (Theobald et al. VLDB04, Fagin et al.
  2001)

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Conclusions

• First attempt to deal with budget constraints.
• For SA only, average precision around 70.
• Tradeoff between RAs and SAs, for relatively low
  cost of RA, RA schedules are improved.

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Thank You !
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(No Transcript)
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Top-k query

• Given a set of n objects and m scoring lists
  sorted in decreasing order, find the top-k
  objects according to a scoring function f
• top-k a set T of k objects such that
  f(rj1,,rjm) f(ri1,,rim) for every object Xi
  in T and every object Xj not in T
• Assumption The scoring function f is monotone
• f(r1,,rm) f(r1,,rm) if ri ri for all I
• Two accesses modes
• sorted access Cs
• random access - Cr
• Objective Compute top-k with the minimum cost

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Sorted Accesses

• Observations
• object with high scores has higher potential to
  be part of the top-k.
• object with mediocre scores does not help.

Prefer high scores
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Example
useless
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Applications

• Mobile Applications
• Highly impatient users, need fast results.
• Mediation Systems
• Achieve high query throughput.
• Online analytics (e.g. logs)
• Achieve high query throughput.

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Motivating Example
Query throughput
Allocate time for each query
Given queries per time unit
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Terminology

1. Sorted Access
2. Random Access
3. highi
4. Top-k queue
5. Candidates queue
6. mink
7. worstScore(d)
8. bestScore(d)

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Efficient Offline Solution- Sorted

• Goal find trace t, such that

L1
L2
B5
t1 0 5
t2 1 4
t3 2 3
t4 3 2
t5 4 1
t6 5 0
Denoted as ROPT
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Efficient Offline Solution- Sorted

• Goal find trace t, such that

B 5
L1
L2
t1 0 5
t2 1 4
t3 2 3
t4 3 2
t5 4 1
t6 5 0

• Feasible for K up to 100, and m up to 10.

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Efficient Offline Solution- Sorted

• Proof (in negation)
• Assume that t does not exists, and chose trace s
  that within the budget and has optimal precision.
  Assume s with traces si that are largest
  position of Pi less or equal to si.
• By construction the score of any object in S is
  the same to S

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Fair Heuristic

• Assume budget b

Runs in batches
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Efficient Offline Solution- Random

• Budget for RAs (B-tCs)

Top-k
o1, S
o2, S
o3, S
o4, S
o10, S
o14, S
.
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Motivation

• Many applications work in budgeted constraint
  environments. Still, they wish to perform top-k
  queries.

Servers
Budget-aware Query processing
Mediator
Engine
User query
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Future work

• Different access costs for different lists
• Time-aware top-k
• Top-k with budget constraints for P2P