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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

Mobile Applications

Highly impatient users, need fast results.

Motivating ExampleMediation Systems

Achieve high query throughput.

Top-k

Top-k

queries

results

Engine

Online Analytics (e.g. logs)

Achieve high query throughput.

Michal Shmueli-Scheuer

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.

sorted

n

m

Michal Shmueli-Scheuer

NRA algorithm (Fagin et al.)

Top-2

Best score

Worst score

highi

f = SUM

mink

candidates

mink > best-score of candidates

Michal Shmueli-Scheuer

NRA algorithm (Fagin et al.)

Top-2

Best score

Worst score

highi

mink

candidates

mink > best-score of candidates

Michal Shmueli-Scheuer

NRA algorithm (Fagin et al.)

Top-2

Best score

Worst score

highi

mink

candidates

mink > best-score of candidates

Michal Shmueli-Scheuer

Access Costs

Sorted access cost- Cs

Random access cost- Cr

Top-k with Budget ConstraintsTop-2

NRA: 12Cs = 12

precision =0.5

Given budget B,

maximize result quality

Cs=1, Cr =3

f = SUM

TA: 7Cs +7Cr = 28

precision =0

Budget =10 ?

Michal Shmueli-Scheuer

Contributions

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

Michal Shmueli-Scheuer

Results Under Limited Budget

Results for limited budget

K results for unlimited

budget

Michal Shmueli-Scheuer

L1

L2

Top-2

o8, SL1

o2, SL2

o1

o4, SL2

P1

o1, SL1

o5

- Interesting positions-where the k objects appear in the lists.

Q1

o5, SL2

o6, SL1

o5, SL1

P2

o3, SL2

o1, SL2

Q2

Efficient Plan- Sorted Accesses

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

- Plan – {L1,4} {L2,2}

Michal Shmueli-Scheuer

L1

L2

o8, SL1

o2, SL2

o4, SL2

P1

o1, SL1

Q1

o5, SL2

o6, SL1

o5, SL1

P2

o3, SL2

o1, SL2

Q2

Plan: {L1,2} {L2,3}

Efficient Plan- Sorted Accesses

- Goal: find plan t, such that :

Plans for B=5

Denoted as ROPT

Michal Shmueli-Scheuer

Sorted Accesses

- Observations:

L1

L2

L3

O1, SL1

O1, SL2

O2, SL1

O2, SL2

O2, SL3

Prefer high scores

Michal Shmueli-Scheuer

Observations – contd.

title=“war” description=“weapon”

Prefer large score reductions

Michal Shmueli-Scheuer

o2, 1

o4, 0.9

o5, 0.8

o3, 0.7

o1, 0.6

Score Utilities

Score gain:

Score reduction:

y =3

Michal Shmueli-Scheuer

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

Michal Shmueli-Scheuer

L1

L2

L3

O1, SL1

O1, SL2

O1, SL3

Adaptive

top-k

o1 [ws,bs]

o2 [ws,bs]

d(o4) = 0.8-0.6=0.2

o3 [0.8,bs]

candidates

hight1

o4 [0.6,bs]

hight2

o6 [ws,bs]

Theobald et al. VLDB04

Michal Shmueli-Scheuer

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….}

precision(schedule1) = precision(schedule2)

Michal Shmueli-Scheuer

o1 [ws,bs]

o2 [ws,bs]

o3 [ws,bs]

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

Michal Shmueli-Scheuer

Gathering with Sorted

Not enough good candidates, RA is wasted

Probing with Random

Not enough RAs to prune the candidates

Random Accesses

- When to switch from SA to RA?

)(

(1-(

time

Michal Shmueli-Scheuer

S+R > B

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.

Michal Shmueli-Scheuer

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

Michal Shmueli-Scheuer

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)

Michal Shmueli-Scheuer

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

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 objectXi in T and every object Xjnot in T
- Assumption: The scoring function f is monotone
- f(r1,…,rm) ≤ f(r1’,…,rm’)ifri ≤ ri’for allI
- Two accesses modes:
- sorted access – Cs
- random access - Cr
- Objective:Compute top-k with the minimum cost

L1

L2

L3

O1, SL1

O1, SL2

O1, SL3

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

Applications

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

Michal Shmueli-Scheuer

Servers

Mediator

Engine

User query

Motivating ExampleQuery throughput

Allocate time for each query

Given #queries

per

time unit

Terminology

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

L1

L2

o8, SL1

o2, SL2

o4, SL2

P1

o1, SL1

P1

o5, SL2

o6, SL1

o5, SL1

P2

o3, SL2

o1, SL2

P2

Efficient Offline Solution- Sorted

- Goal: find trace t, such that :

L1

L2

B=5

Denoted as ROPT

L1

L2

o8, SL1

o2, SL2

o4, SL2

P1

o1, SL1

P1

o5, SL2

o6, SL1

o5, SL1

P2

o3, SL2

o1, SL2

P2

Efficient Offline Solution- Sorted

- Goal: find trace t, such that :

B =5

L1

L2

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

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`

d Rexact

best(o)-mink

(best(o) = wosrt(o)+RA)

o5, S

o8, S

o7, S

o9, S

….

….

Efficient Offline Solution- Random

- Budget for RAs =(B-|t|*Cs)

Top-k

o1, S

o2, S

o3, S

o4, S

o10, S

o14, S

….

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

Future work

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

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