1. 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

2. Motivating Example Mediation Systems Achieve high query throughput.
Top-k
Top-k
queries
results
Engine
Mobile Applications
Highly impatient users, need fast results.
Online Analytics (e.g. logs)
Achieve high query throughput.
Michal Shmueli-Scheuer

3. Traditional top-k query
0.9 b
0.6 c
0.5 … .. d
0.4 R2 d
0.87 a
0.85 f
0.5 … .. c
0.2 Rm c
0.9 b
0.6 g
0.5 … .. a
0.4
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.
sorted n m
Michal Shmueli-Scheuer

4. NRA algorithm (Fagin et al.)
0.9 b
0.6 c
0.5 … .. d
0.4 R2 d
0.87 a
0.85 f
0.5 …. .. c
0.2
Top-2
Best score
Worst score
highi a
[0.9,1.77] d
[0.87,1.77]
f = SUM
mink
candidates
Add summation
mink > best-score of candidates
Michal Shmueli-Scheuer

5. NRA algorithm (Fagin et al.)
0.9 b
0.6 c
0.5 … .. d
0.4 R2 d
0.87 a
0.85 f
0.25 …. .. c
0.2
Top-2
Best score
Worst score a
[1.75,1.75] d
[0.87,1.47]
highi
mink
candidates b
[0.6,1.45]
mink > best-score of candidates
Michal Shmueli-Scheuer

6. NRA algorithm (Fagin et al.)
0.9 b
0.6 c
0.5 … .. d
0.4 R2 d
0.87 a
0.85 f
0.25 …. .. c
0.2
Top-2
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 > best-score of candidates
Michal Shmueli-Scheuer

7. Top-k with Budget Constraints
Access Costs
Sorted access cost- Cs
Random access cost- Cr R1 s
0.95 u
0.93 t
0.92 d
0.9 x
0.5 y
0.4 z
0.2 … R2 a
1.0 b
0.9 c
0.85 d
0.8 e
0.7 t
0.6 f
0.4 .. d
1.7 t
1.52
NRA: 12Cs = 12
precision =0.5
Given budget B,
maximize result quality
Cs=1, Cr =3
f = SUM
TA: 7Cs +7Cr = 28
precision =0
-change green
- First NRA (then TA)
Budget =10 ?
Michal Shmueli-Scheuer

8. Contributions Sorted Accesses Sorted and Random Accesses Experiments
Efficient Plan
Solution with Adaptive a
Sorted and Random Accesses
Experiments
-title” out contributions
Michal Shmueli-Scheuer

9. Results Under Limited Budget
Results for limited budget
K results for unlimited
budget
=remove lemma
Michal Shmueli-Scheuer

10. Efficient Plan- Sorted Accesses
Assume that we know the k results for unlimited budget (REXACT). L1 L2
o1, SL1
o1, SL2
o5, SL1
o2, SL2
o5, SL2
o4, SL2
o8, SL1
o6, SL1
o3, SL2
Plan – {L1,4} {L2,2} o5 o1
Top-2 P1 P2 Q1 Q2
Interesting positions- where the k objects appear in the lists.
Sorted accesRemove offline
- plan instead of trace
P and Q
- add animation what is a plan (allocation of resource)
Michal Shmueli-Scheuer

11. Efficient Plan- Sorted Accesses
Goal: find plan t, such that :
Plans for B=5 P1 P2 Q1 Q2 L1 L2
o1, SL1
o1, SL2
o5, SL1
o2, SL2
o5, SL2
o4, SL2
o8, SL1
o6, SL1
o3, SL2
=remove lemma
Plan: {L1,2} {L2,3}
Denoted as ROPT
Michal Shmueli-Scheuer

12. Sorted Accesses Observations: Prefer high scores L1 L2 L3 O1, SL1
- Remove the sentences add another object
Prefer high scores
Michal Shmueli-Scheuer

13. Prefer large score reductions
Observations – contd.
title=“war” description=“weapon”
observation
Prefer large score reductions
Michal Shmueli-Scheuer

14. Score Utilities Score gain: Score reduction: o2, 1 o4, 0.9 y =3
Remove formula
-split it into 2 slides
Michal Shmueli-Scheuer

15. Optimization Problem Bi-objective optimization problem:
util(Li,x) = a* gain +(1-a)* reduction
Different color
Remove icde add name
Put num of slides out of
Remove formula
-split it into 2 slides
Heuristics:
Fair Heuristic
Rank Heuristic
Where m is the number of lists
Michal Shmueli-Scheuer

16. Adaptive 
gain
reduction
))
(1-(
time
Michal Shmueli-Scheuer

17. Adaptive  d(o4) = 0.8-0.6=0.2 top-k o1 [ws,bs] L1 L2 L3 O1, SL1
o3 [0.8,bs]
d(o4) = =0.2
candidates
hight1
o4 [0.6,bs]
hight2
o6 [ws,bs]
Theobald et al. VLDB04
Michal Shmueli-Scheuer

18. Adaptive 
TREC query, k=100
Michal Shmueli-Scheuer

19. Efficient Plan- Random Accesses
Observations:
random accesses occur always after sorted accesses have been finished.
schedule 1: {SA……RA……SA….}
schedule 2: {SA……SA……RA….}
Add access
precision(schedule1) = precision(schedule2)
Michal Shmueli-Scheuer

20. Observations- contd.
Random accesses are only useful to objects in REXACT.
top-k L2
o1 [ws,bs]
o2 [ws,bs]
o3 [ws,bs]
o1 [ws,bs]
o2, SL2
Precision reduced
o5 [ws,bs]
o5, Not in REXACT
o2 [ws,bs]
o5, SL2
candidates
o4 [ws,bs]
Precision remains the same
o5 [ws,bs]
o1, SL2
Michal Shmueli-Scheuer

21. Random Accesses When to switch from SA to RA? Gathering with Sorted
Probing with Random
)(
Not enough good candidates, RA is wasted
Stress that RA is much more expensive then SA. Why we do last
(1-(
Not enough RAs to prune the candidates
time
Michal Shmueli-Scheuer

22. Random Accesses Switch from Sorted to Random: R= (1- )*S
S – total cost of sorted accesses.
R – total cost for random accesses.
S+R > B
Which items to access ?
Do one 1 RA on each candidate.
maximize expected score.
Michal Shmueli-Scheuer

23. Experimental Data Zipf, #lists =[2,6], #objects =[10000,1000000]
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, ]
Aggregate Function : Sum
Aggregate function: Sum
Michal Shmueli-Scheuer

24. Evaluation Methods percentage of optimal precision SME Ropt Rexact
Ralg
Ropt
SME
Michal Shmueli-Scheuer

25. Results- Sorted Accesses
TREC, k=100
Less budget, more improvement
Michal Shmueli-Scheuer

26. Varied k
IMDB, B=400
Lower K, more improvement.
Michal Shmueli-Scheuer

27. Number of Lists More lists, more improvement. Zipf, K=100, B=4000
Michal Shmueli-Scheuer

28. Results- Random Accesses
TREC, k=100,Cr=10
TREC, K=100, Cr=100

29. 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)
-move it to later
Michal Shmueli-Scheuer

30. 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.
Michal Shmueli-Scheuer

31. Thank You !

33. 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

34. Sorted Accesses Observations:
object with high scores has higher potential to be part of the top-k.
object with “mediocre” scores does not help. L1 L2 L3
O1, SL1
O1, SL2
O1, SL3
- Remove the sentences add another object
Prefer high scores

35. Example
Wireless zone Q
useless

36. Applications Mobile Applications Mediation Systems
Highly impatient users, need fast results.
Mediation Systems
Achieve high query throughput.
Online analytics (e.g. logs)
Michal Shmueli-Scheuer

37. Motivating Example Query throughput Given #queries per time unit
Mediator
Servers
User query
Engine
Query throughput
Allocate time for each query
Given #queries
per
time unit

38. Terminology Sorted Access Random Access highi Top-k queue
Candidates queue
mink
worstScore(d)
bestScore(d)

39. Efficient Offline Solution- Sorted
Goal: find trace t, such that : L1 L2 P1 P2 L1 L2
o1, SL1
o1, SL2
o5, SL1
o2, SL2
o5, SL2
o4, SL2
o8, SL1
o6, SL1
o3, SL2
B=5 t1 5 t2 1 4 t3 2 3 t4 t5 t6
=remove lemma
Denoted as ROPT

40. Efficient Offline Solution- Sorted
Goal: find trace t, such that :
B =5 L1 L2 P1 P2 L1 L2
o1, SL1
o1, SL2
o5, SL1
o2, SL2
o5, SL2
o4, SL2
o8, SL1
o6, SL1
o3, SL2 t1 5 t2 1 4 t3 2 3 t4 t5 t6
Feasible for K up to 100, and m up to 10.

41. 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 s`i 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`

42. Fair Heuristic Assume budget =b Runs in batches
Explain the “absolute value”. Explain here the batches

43. Efficient Offline Solution- Random
Budget for RAs =(B-|t|*Cs)
Top-k
d Rexact
o9, S
o5, S
o7, S
o8, S ….
best(o)-mink
(best(o) = wosrt(o)+RA)
o1, S
o2, S
o3, S
o4, S
o10, S
o14, S ….

44. 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

45. Future work Different access costs for different lists
Time-aware top-k
Top-k with budget constraints for P2P