Bit-parallel ( δ , γ ) -matching and suffix automata
( δ , γ ) -matching is a string matching problem with applications to music retrieval. The goal is, given a pattern P 1 … m and a text T 1 … n on an alphabet of integers, find the occurrences P ′ of the pattern in the text such that (i) ∀ 1 ⩽ i ⩽ m , | P i − P i ′ | ⩽ δ , and (ii) ∑ 1 ⩽ i ⩽ m | P i...
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| Vydané v: | Journal of discrete algorithms (Amsterdam, Netherlands) Ročník 3; číslo 2; s. 198 - 214 |
|---|---|
| Hlavní autori: | , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier B.V
2005
Elsevier |
| Predmet: | |
| ISSN: | 1570-8667, 1570-8675 |
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| Abstract | (
δ
,
γ
)
-matching is a string matching problem with applications to music retrieval. The goal is, given a pattern
P
1
…
m
and a text
T
1
…
n
on an alphabet of integers, find the occurrences
P
′
of the pattern in the text such that (i)
∀
1
⩽
i
⩽
m
,
|
P
i
−
P
i
′
|
⩽
δ
, and (ii)
∑
1
⩽
i
⩽
m
|
P
i
−
P
i
′
|
⩽
γ
. The problem makes sense for
δ
⩽
γ
⩽
δ
m
. Several techniques for
(
δ
,
γ
)
-matching have been proposed, based on bit-parallelism or on skipping characters. We first present an
O
(
m
n
log
(
γ
)
/
w
)
worst-case time and
O
(
n
)
average-case time bit-parallel algorithm (being
w the number of bits in the computer word). It improves the previous
O
(
m
n
log
(
δ
m
)
/
w
)
worst-case time algorithm of the same type. Second, we combine our bit-parallel algorithm with suffix automata to obtain the first algorithm that skips characters using both
δ and
γ. This algorithm examines less characters than any previous approach, as the others do just
δ-matching and check the
γ-condition on the candidates. We implemented our algorithms and drew experimental results on real music, showing that our algorithms are superior to current alternatives with high values of
δ. |
|---|---|
| AbstractList | (
δ
,
γ
)
-matching is a string matching problem with applications to music retrieval. The goal is, given a pattern
P
1
…
m
and a text
T
1
…
n
on an alphabet of integers, find the occurrences
P
′
of the pattern in the text such that (i)
∀
1
⩽
i
⩽
m
,
|
P
i
−
P
i
′
|
⩽
δ
, and (ii)
∑
1
⩽
i
⩽
m
|
P
i
−
P
i
′
|
⩽
γ
. The problem makes sense for
δ
⩽
γ
⩽
δ
m
. Several techniques for
(
δ
,
γ
)
-matching have been proposed, based on bit-parallelism or on skipping characters. We first present an
O
(
m
n
log
(
γ
)
/
w
)
worst-case time and
O
(
n
)
average-case time bit-parallel algorithm (being
w the number of bits in the computer word). It improves the previous
O
(
m
n
log
(
δ
m
)
/
w
)
worst-case time algorithm of the same type. Second, we combine our bit-parallel algorithm with suffix automata to obtain the first algorithm that skips characters using both
δ and
γ. This algorithm examines less characters than any previous approach, as the others do just
δ-matching and check the
γ-condition on the candidates. We implemented our algorithms and drew experimental results on real music, showing that our algorithms are superior to current alternatives with high values of
δ. (δ,γ)-matching is a string matching problem with applications to music retrieval. The goal is, given a pattern P1...m and a text T1...n on an alphabet of integers, find the occurrences P′ of the pattern in the text such that (i) ∇1≤i≤m, |Pi-P'i|≤δ and (ii) ∑1≤i≤m|Pi-P'i|≤γ. The problem makes sense for δ≤γ≤δm. Several techniques for (δ,γ)-matching have been proposed, based on bit-parallelism or on skipping characters. We first present an O(mn log(γ) / w) worst-case time and O(n) average-case time bit-parallel algorithm (being w the number of bits in the computer word). It improves the previous O(mn log(δm) / w) worst-case time algorithm of the same type. Second, we combine our bit-parallel algorithm with suffix automata to obtain the first algorithm that skips characters using both δ and γ. This algorithm examines less characters than any previous approach, as the others do just δ-matching and check the γ-condition on the candidates. We implemented our algorithms and drew experimental results on real music, showing that our algorithms are superior to current alternatives with high values of δ. |
| Author | Pinzon, Yoan J. Iliopoulos, Costas S. Crochemore, Maxime Navarro, Gonzalo Salinger, Alejandro |
| Author_xml | – sequence: 1 givenname: Maxime surname: Crochemore fullname: Crochemore, Maxime email: mac@univ-mlv.fr organization: Institut Gaspard-Monge, Université de Marne-la-Vallée, France – sequence: 2 givenname: Costas S. surname: Iliopoulos fullname: Iliopoulos, Costas S. email: csi@dcs.kcl.ac.uk organization: Department of Computer Science, King's College, London, England, UK – sequence: 3 givenname: Gonzalo surname: Navarro fullname: Navarro, Gonzalo email: gnavarro@dcc.uchile.cl organization: Center for Web Research, Department of Computer Science, University of Chile, Chile – sequence: 4 givenname: Yoan J. surname: Pinzon fullname: Pinzon, Yoan J. email: pinzon@dcs.kcl.ac.uk organization: Department of Computer Science, King's College, London, England, UK – sequence: 5 givenname: Alejandro surname: Salinger fullname: Salinger, Alejandro email: asalinge@dcc.uchile.cl organization: Center for Web Research, Department of Computer Science, University of Chile, Chile |
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| Cites_doi | 10.1007/s00453-001-0034-6 10.1145/359842.359859 10.1080/00207160213939 10.1145/79173.79184 10.1006/inco.1994.1007 10.1145/135239.135244 10.1007/BF01185427 10.1007/PL00009253 10.1145/135239.135243 |
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| Keywords | Approximate string matching Bit-parallelism MIDI music retrieval approximate string matching bit-parallelism |
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| References | Crochemore, Rytter (bib012) 1994 Crochemore, Iliopoulos, Lecroq, Plandowski, Rytter (bib011) 2002; vol. 2373 Navarro, Baeza-Yates (bib016) 2001; 30 Baeza-Yates, Navarro (bib004) 1999; 23 P. McGettrick, MIDIMatch: Musical pattern matching in real time, MSc Dissertation, York University, UK, 1997 Crochemore, Iliopoulos, Lecroq, Pinzon, Plandowski, Rytter (bib010) 2003; 55 Roland, Ganascia (bib019) 2000 Cambouropoulos, Crochemore, Iliopoulos, Mouchard, Pinzon (bib007) 1999 Crawford, Iliopoulos, Raman (bib009) 1998; 11 Cambouropoulos, Crochemore, Iliopoulos, Mouchard, Pinzon (bib008) 2002; 79 Baeza-Yates (bib001) 1992 Navarro, Raffinot (bib018) 2002 Boyer, Moore (bib005) 1977; 20 Baeza-Yates, Gonnet (bib003) 1994; 108 Lemström, Navarro (bib014) 2003; vol. 2857 Smith, Chiu, Scott (bib020) 2000 Cambouropoulos, Crawford, Iliopoulos (bib006) 1999 Baeza-Yates, Gonnet (bib002) 1992; 35 Wu, Manber (bib023) 1992; 35 Czumaj, Crochemore, Gasieniec, Jarominek, Lecroq, Plandowski, Rytter (bib013) 1994; 12 Navarro, Raffinot (bib017) 2000; 5 Sunday (bib021) 1990; 33 Ukkonen (bib022) 1993 Baeza-Yates (10.1016/j.jda.2004.08.005_bib003) 1994; 108 Navarro (10.1016/j.jda.2004.08.005_bib016) 2001; 30 Crawford (10.1016/j.jda.2004.08.005_bib009) 1998; 11 Czumaj (10.1016/j.jda.2004.08.005_bib013) 1994; 12 Sunday (10.1016/j.jda.2004.08.005_bib021) 1990; 33 Baeza-Yates (10.1016/j.jda.2004.08.005_bib002) 1992; 35 Roland (10.1016/j.jda.2004.08.005_bib019) 2000 Lemström (10.1016/j.jda.2004.08.005_bib014) 2003; vol. 2857 Cambouropoulos (10.1016/j.jda.2004.08.005_bib007) 1999 Crochemore (10.1016/j.jda.2004.08.005_bib011) 2002; vol. 2373 Crochemore (10.1016/j.jda.2004.08.005_bib012) 1994 Baeza-Yates (10.1016/j.jda.2004.08.005_bib001) 1992 Cambouropoulos (10.1016/j.jda.2004.08.005_bib006) 1999 Cambouropoulos (10.1016/j.jda.2004.08.005_bib008) 2002; 79 Crochemore (10.1016/j.jda.2004.08.005_bib010) 2003; 55 Navarro (10.1016/j.jda.2004.08.005_bib018) 2002 Boyer (10.1016/j.jda.2004.08.005_bib005) 1977; 20 10.1016/j.jda.2004.08.005_bib015 Smith (10.1016/j.jda.2004.08.005_bib020) 2000 Wu (10.1016/j.jda.2004.08.005_bib023) 1992; 35 Navarro (10.1016/j.jda.2004.08.005_bib017) 2000; 5 Baeza-Yates (10.1016/j.jda.2004.08.005_bib004) 1999; 23 Ukkonen (10.1016/j.jda.2004.08.005_bib022) 1993 |
| References_xml | – volume: 35 start-page: 74 year: 1992 end-page: 82 ident: bib002 article-title: A new approach to text searching publication-title: Comm. ACM – volume: 30 start-page: 473 year: 2001 end-page: 502 ident: bib016 article-title: Improving an algorithm for approximate string matching publication-title: Algorithmica – volume: 35 start-page: 83 year: 1992 end-page: 91 ident: bib023 article-title: Fast text searching allowing errors publication-title: Comm. ACM – reference: P. McGettrick, MIDIMatch: Musical pattern matching in real time, MSc Dissertation, York University, UK, 1997 – start-page: 228 year: 1993 end-page: 242 ident: bib022 article-title: Approximate string matching over suffix trees publication-title: Proc. 4th Ann. 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ACM doi: 10.1145/135239.135244 – volume: 12 start-page: 247 year: 1994 ident: 10.1016/j.jda.2004.08.005_bib013 article-title: Speeding up two string-matching algorithms publication-title: Algorithmica doi: 10.1007/BF01185427 – start-page: 165 year: 2000 ident: 10.1016/j.jda.2004.08.005_bib020 article-title: A speech interface for building musical score collections – volume: 23 start-page: 127 issue: 2 year: 1999 ident: 10.1016/j.jda.2004.08.005_bib004 article-title: Faster approximate string matching publication-title: Algorithmica doi: 10.1007/PL00009253 – ident: 10.1016/j.jda.2004.08.005_bib015 – volume: 55 start-page: 1 year: 2003 ident: 10.1016/j.jda.2004.08.005_bib010 article-title: Occurrence and substring heuristics for δ-matching publication-title: Fundamenta Informaticae – volume: 35 start-page: 74 issue: 10 year: 1992 ident: 10.1016/j.jda.2004.08.005_bib002 article-title: A new approach to text searching publication-title: Comm. ACM doi: 10.1145/135239.135243 – year: 1994 ident: 10.1016/j.jda.2004.08.005_bib012 – start-page: 465 year: 1992 ident: 10.1016/j.jda.2004.08.005_bib001 article-title: Text retrieval: Theory and practice – year: 2002 ident: 10.1016/j.jda.2004.08.005_bib018 – start-page: 228 year: 1993 ident: 10.1016/j.jda.2004.08.005_bib022 article-title: Approximate string matching over suffix trees |
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δ
,
γ
)
-matching is a string matching problem with applications to music retrieval. The goal is, given a pattern
P
1
…
m
and a text
T
1
…
n
on an alphabet... (δ,γ)-matching is a string matching problem with applications to music retrieval. The goal is, given a pattern P1...m and a text T1...n on an alphabet of... |
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| SubjectTerms | Approximate string matching Bit-parallelism Computer Science Data Structures and Algorithms MIDI music retrieval |
| Title | Bit-parallel ( δ , γ ) -matching and suffix automata |
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