Transcript PPT - Jiaheng Lu

Efficient Merging and
Filtering Algorithms for
Approximate String Searches
Jiaheng Lu,
University of California, Irvine
Joint work with Chen Li, Yiming Lu
1
Example: a movie database
Find movies starred Schwarrzenger.
Star
Keanu Reeves
Title
The Matrix
Year
1999
Genre
Sci-Fi
Samuel Jackson
Iron man
2008
Sci-Fi
Schwarzenegger
The Terminator
1984
Sci-Fi
Samuel Jackson
The man
2006
Crime
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In general:
Gap between Queries and Data

Errors in the query


The user doesn’t remember a string exactly
The user unintentionally types a wrong string
Query: Schwarrzenger.
Data : Schwarzenegger
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…
…
Data may not clean

Errors in the database:

Data often is not clean by itself, especially true in data
integration and cleansing
Relation R
Star
Relation S
Star
Keanu Reeves
Keanu Reeves
Samuel Jackson
Samuel L. Jackson
Schwarzenegger
Schwarzenegger
Samuel Jackson
Samuel L. Jackson
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Query may include error
5
Problem definition:
approximate string searches
Collection of strings s
Search
Query q
Star
Keanu Reeves
Samuel Jackson
Schwarzenegger
Samuel Jackson
…
Output: strings s that satisfy Sim(q,s)≤δ
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Example Similarity Function:
Edit Distance



A widely used metric to define string similarity
Ed(s1,s2)= minimum # of operations (insertion,
deletion, substitution) to change s1 to s2
Example:
s1: Tom Hanks
s2: Ton Hank
ed(s1,s2) = 2
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Example: approximate string searches
Collection of strings s
Search
Query q
Tom Hanks
Star
Tom Hank
Thomas Hanks
Ton Hank
Tom J. Hanks
…
Output: strings s that satisfy ed(q,s)≤2
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Outline
Problem motivation
 Preliminary



Grams
Inverted lists
Merge algorithms
 Filtering technique
 Conclusion

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String  Grams

q-grams
For example: 2-gram
u
n
i
v
e
r
s
a
l
(un),(ni),(iv),(ve),(er),(rs),(sa),(al)
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Inverted lists

Convert strings to gram inverted lists
id
0
1
2
3
4
strings
rich
stick
stich
stuck
static
2-grams
at
ch
ck
ic
ri
st
ta
ti
tu
uc
4
0
2
1
0
0
1
4
1
3
3
3
1
2
4
2
3
4
2
4
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Main Example
Query
ed(s,q)≤1
stick
(st,ti,ic,ck)
Grams
Data
id
strings
0
rich
1
stick
2
stich
3
stuck
4
static
st
1,2,3,4
ti
1,2,4
ic
0,1,2,4
ck
1,3
Merge
Candidate string ids
{1,2,3,4}
count >=2
Double check
for the real
edit distance
ck
1,3
ic
0,1,2,4
Final answers
st
1,2,3,4
{1,2,3}
ta
4
ti
…
1,2,4
Performance
bottleneck!
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Sub-problem definitions:
Given multiple inverted lists with
integer values in increasing order
and a threshold T, we find all values
whose number of occurrences ≥ T.
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Example

Count threshold: 4
1
10
5
3
13
7
5
15
13
13
15
10
13
Result: 13
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Outline
Problem motivation
 Preliminary
 Merge algorithms



Two previous algorithms
Our proposed three algorithms
Filtering technique
 Conclusion

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Five Merge Algorithms
HeapMerger
MergeOpt
[Sarawagi,SIGMOD
2004]
[Sarawagi,SIGMOD
2004]
Previous
New
ScanCount
MergeSkip
DivideSkip
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Two previous algorithms (1)
Heap-based Algorithm
Push to
heap
……
Min-heap
Count # of the occurrences of each element by a heap
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Example of HeapMerger
[Sarawagi et al 2004]
1
minHeap
10
13
5
15
1
10
5
3
13
7
5
15
13
13
15
10
13
Count threshold ≥ 4
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Five Merge Algorithms
MergeOpt
HeapMerger
[Sarawagi 2004]
[Sarawagi 2004]
Previous
New
ScanCount
MergeSkip
DivideSkip
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Two previous algorithms (2)
MergeOpt Algorithm
Binary
search
Long Lists: T-1
Short Lists
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Example of MergeOpt
[Sarawagi et al 2004]
Min-heap
1
10
5
3
13
7
5
15
13
13
15
10
13
Long Lists: 3
Short Lists: 2
Count threshold ≥ 4
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Can we run faster?
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Five Merge Algorithms
HeapMerger
MergeOpt
Previous
New
ScanCount
MergeSkip
DivideSkip
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Our new algorithms (1)
ScanCount Algorithm
Use an array to record # of occurrences of each
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element
ScanCount Example
1
2
3
4
5
6 7
8
9 10 11 12 13 14 15
1 0 1 0 2 0 1 0 0 2 0 0 4 0 1
Result:13
1
10
5
3
13
7
5
15
13
13
15
10
13
Count threshold ≥ 4
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Five Merge Algorithms
HeapMerger
MergeOpt
Previous
New
ScanCount
MergeSkip
DivideSkip
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Our new algorithms (2)
MergeSkip algorithm
……
Min-heap
Pop T-1
Jump
T-1
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Example of MergeSkip
minHeap
1
10
5
3
13
7
5
15
13
13
15
10
13
Count threshold ≥ 4
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Example of MergeSkip
1
minHeap
5
13
10
15
1
10
5
3
13
7
5
15
13
13
15
10
13
Count threshold ≥ 4
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Example of MergeSkip
minHeap
Pop 1, 5,10
13
15
1
10
5
3
13
7
5
15
13
13
15
10
13
Count threshold ≥ 4
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Example of MergeSkip
minHeap
Pop 1, 5,10
13
15
1
10
5
Jump
3
13
7
≥ 13
5
15
13
13
15
10
13
Count threshold ≥ 4
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Example of HeapMerger
minHeap
13
13
13
13
15
1
10
5
3
13
7
5
15
13
13
15
Result:13
10
13
Count threshold ≥ 4
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Five Merge Algorithms
HeapMerger
MergeOpt
Previous
New
ScanCount
MergeSkip
DivideSkip
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Our new algorithms (3)
DivideSkip Algorithm
MergeSkip
Binary
search
Long Lists: dynamic size
Short Lists
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Size of long lists
How many lists are treated as long lists?
Cost:
MergeOpt
Binary
search
Long Lists
Short Lists
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Size of long lists
How many lists are treated as long lists?
Cost:
MergeSkip
Binary
search
Long Lists
Short Lists
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Decide L value
A good balance in the tradeoff:
# of long lists = T / ( μ logM +1)
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Empirically verification
Our formula about “L” achieves the best
result over other options.
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Experimental data sets
Three real data sets have various string
lengths and data sizes
DBLP data
IMDB data
Google Web
corpus
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Performance (DBLP data)
DivideSkip
is the best
one
Running time per query with various algorithms
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# of elements reading (DBLP data)
DivideSkip
is the best
one
DivideSkip skips reading the most elements
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Outline
Problem motivation
 Preliminary
 Merge algorithms
 Filtering technique




Length, positional filter [Gravano et al. VLDB 2001]
Filter tree
Conclusion and future work
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Length Filtering
Length: 10
s:
By length
only!
Ed(s,t) ≤ 2
t:
Length: 19
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Positional Filtering

Positional Gram


For example: string abcd:
{(ab,1),(bc,2),(cd,3)}
Ed(s,t) ≤ 2
s
a b
(ab,1)
t
a b
(ab,12)
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Filter tree
root
1
2
aa
ab
3
…
…
zy
1
2
5
12
17
28
44
n
Gram level
zz
…
Length level
m
Position level
Inverted list
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Surprising experimental results(DBLP)
Heap
MergeOpt
No filter
Length
115.42
11.98
Length+Pos
3.64
Wisely
use
14.22
1.40 filters,
6.78
more filters may be bad!
ScanCount
30.91
2.68
2.14
MergeSkip
10.12
1.09
2.65
DivideSkip
2.23
0.76
1.96
Conclusion
 Three

new merge algorithms
We run faster
 Surprising
experimental results
Wisely use filters,
more filters may be bad!
Thank you!
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Backup : related work
Approximate
string matching
[Navarro 2001]
Fuzzy lookup in
Varied length
Grams
[Li et al 2007]
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Reference
1.
2.
3.
[Arasu 2006] A. Arasu and V. Ganti and R.
Kaushik “Efficient Exact Set-similarity Joins” in
VLDB 2006
[Chaudhuri 2003] S. Chaudhuri ,K Ganjam, V.
Ganti and R. Motwani “Robust and Efficient
Fuzzy Match for online Data Cleaning” in
SIGMOD 2003
[Gravano 2001] L. Gravano, P.G. Ipeirotis, H.V.
Jagadish, N. Koudas, S. Muthukrishnan and D.
Srivastava “Approximate string joins in a
database almost for free” in VLDB 2001
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Reference
4. [Li 2007] C. Li, B Wang and X. Yang
“VGRAM:Improving performance of approximate
queries on string collections using variablelength grams ” in VLDB 2007
5. [Navarro 2001] G. Navarro, “A guided tour to
approximate string matching” in Computing
survey 2001
6. [Sarawagi 2004] S. Sarawagi and A. Kirpal,
“Efficient set joins on similarity predicates” in
ACM SIGMOD 2004
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