Approximate swapped matching
Let a text string T of n symbols and a pattern string P of m symbols from alphabet Σ be given. A swapped version P′ of P is a length m string derived from P by a series of local swaps (i.e., p′ ℓ← p ℓ+1 and p′ ℓ+1← p ℓ), where each element can participate in no more than one swap. The Pattern Matchi...
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| Vydané v: | Information processing letters Ročník 83; číslo 1; s. 33 - 39 |
|---|---|
| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Amsterdam
Elsevier B.V
16.07.2002
Elsevier Science Elsevier Sequoia S.A |
| Predmet: | |
| ISSN: | 0020-0190, 1872-6119 |
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| Abstract | Let a text string
T of
n symbols and a pattern string
P of
m symbols from alphabet
Σ be given. A
swapped version
P′ of
P is a length
m string derived from
P by a series of
local swaps (i.e.,
p′
ℓ←
p
ℓ+1 and
p′
ℓ+1←
p
ℓ), where each element can participate in
no more than one swap. The
Pattern Matching with Swaps problem is that of finding all locations
i of
T for which there exists a swapped version
P′ of
P with an exact matching of
P′ in location
i of
T.
Recently, some efficient algorithms were developed for this problem. Their time complexity is better than the best known algorithms for pattern matching with mismatches. However, the
Approximate Pattern Matching with Swaps problem was not known to be solved faster than the
Pattern Matching with Mismatches problem.
In the
Approximate Pattern Matching with Swaps problem the output is, for every text location
i where there is a swapped match of
P, the
number of swaps necessary to create the swapped version that matches location
i. The fastest known method to-date is that of counting mismatches and dividing by two. The time complexity of this method is
O(n
m
logm
)
for a general alphabet
Σ.
In this paper we show an algorithm that counts the number of swaps at every location where there is a swapped matching in time O(
nlog
mlog
σ), where
σ=min(
m,|
Σ|). Consequently, the total time for solving the approximate pattern matching with swaps problem is O(
f(
n,
m)+
nlog
mlog
σ), where
f(
n,
m) is the time necessary for solving the
Pattern Matching with Swaps problem. Since
f(
n,
m) was shown to be O(
nlog
mlog
σ) this means our algorithm's running time is O(
nlog
mlog
σ). |
|---|---|
| AbstractList | Let a text string T of n symbols and a pattern string P of m symbols from alphabet E be given. A swapped version P' of P is a length m string derived from P by a series of local swaps, where each element can participate in no more than one swap. The Pattern Matching with Swaps problem is that of finding all locations i of T for which there exists a swapped version P' of P with an exact matching of P' in location i of T. Some efficient algorithms were developed for this problem. Their time complexity is better than the best known algorithms for pattern matching with mismatches. The Approximate Pattern Matching with Swaps problem was not known to be solved faster than the Pattern Matching with Mismatches problem. Let a text string T of n symbols and a pattern string P of m symbols from alphabet Σ be given. A swapped version P′ of P is a length m string derived from P by a series of local swaps (i.e., p′ ℓ← p ℓ+1 and p′ ℓ+1← p ℓ), where each element can participate in no more than one swap. The Pattern Matching with Swaps problem is that of finding all locations i of T for which there exists a swapped version P′ of P with an exact matching of P′ in location i of T. Recently, some efficient algorithms were developed for this problem. Their time complexity is better than the best known algorithms for pattern matching with mismatches. However, the Approximate Pattern Matching with Swaps problem was not known to be solved faster than the Pattern Matching with Mismatches problem. In the Approximate Pattern Matching with Swaps problem the output is, for every text location i where there is a swapped match of P, the number of swaps necessary to create the swapped version that matches location i. The fastest known method to-date is that of counting mismatches and dividing by two. The time complexity of this method is O(n m logm ) for a general alphabet Σ. In this paper we show an algorithm that counts the number of swaps at every location where there is a swapped matching in time O( nlog mlog σ), where σ=min( m,| Σ|). Consequently, the total time for solving the approximate pattern matching with swaps problem is O( f( n, m)+ nlog mlog σ), where f( n, m) is the time necessary for solving the Pattern Matching with Swaps problem. Since f( n, m) was shown to be O( nlog mlog σ) this means our algorithm's running time is O( nlog mlog σ). |
| Author | Amir, Amihood Lewenstein, Moshe Porat, Ely |
| Author_xml | – sequence: 1 givenname: Amihood surname: Amir fullname: Amir, Amihood email: amir@cs.biu.ac.il organization: Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel – sequence: 2 givenname: Moshe surname: Lewenstein fullname: Lewenstein, Moshe email: moshe@cs.biu.ac.il organization: Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel – sequence: 3 givenname: Ely surname: Porat fullname: Porat, Ely email: porately@cs.biu.ac.il organization: Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel |
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| Cites_doi | 10.1137/0222053 10.1126/science.270.5235.394 10.1137/0206024 10.1006/jagm.2000.1120 10.1016/S0020-0190(98)00151-3 10.1137/S0097539794264810 10.1137/0216067 10.1006/inco.1995.1047 10.1016/0196-6774(89)90010-2 10.1006/inco.1995.1144 10.1137/0219067 |
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| Keywords | Pattern matching with swaps Non-standard pattern matching Combinatorial algorithms on words Design and analysis of algorithms Pattern matching Approximate pattern matching Design Word Combinatorial problem Combinatorial algorithm Nonstandard analysis Algorithm Algorithm analysis |
| Language | English |
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| Snippet | Let a text string
T of
n symbols and a pattern string
P of
m symbols from alphabet
Σ be given. A
swapped version
P′ of
P is a length
m string derived from
P by... Let a text string T of n symbols and a pattern string P of m symbols from alphabet E be given. A swapped version P' of P is a length m string derived from P by... |
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| SubjectTerms | Algebra Algorithms Applied sciences Approximate pattern matching Artificial intelligence Classical and quantum physics: mechanics and fields Classical combinatorial problems Classical mechanics of discrete systems: general mathematical aspects Combinatorial algorithms on words Combinatorics Combinatorics. Ordered structures Computer programming Computer science; control theory; systems Design and analysis of algorithms Exact sciences and technology Mathematics Non-standard pattern matching Number theory Pattern matching Pattern matching with swaps Pattern recognition. Digital image processing. Computational geometry Physics Sciences and techniques of general use Studies |
| Title | Approximate swapped matching |
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