Abstract
We consider the approximability of three recently introduced pattern matching problems which have been shown to be NP-hard. Given two strings as input, the first problem is to find the longest common parameterised subsequence between two strings. The second is a maximisation variant of generalised function matching and the third is a a maximisation variant of generalised parameterised matching. We show that in all three cases there exists an ∈ > 0 such that there is no polynomial time (1 - ∈)-approximation algorithm, unless P = NP. We then present a polynomial time √ 1/OPT-approximation algorithm for a variant of generalised parameterised matching for which no previous approximation results are known.
| Original language | English |
|---|---|
| Title of host publication | Proceedings of the Prague Stringology Conference 2010 |
| Pages | 52-62 |
| Number of pages | 11 |
| Publication status | Published - 2010 |
| Externally published | Yes |
| Event | Prague Stringology Conference 2010, PSC 2010 - Prague, Czech Republic Duration: Aug 30 2010 → Sep 1 2010 |
Other
| Other | Prague Stringology Conference 2010, PSC 2010 |
|---|---|
| Country | Czech Republic |
| City | Prague |
| Period | 8/30/10 → 9/1/10 |
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ASJC Scopus subject areas
- Mathematics(all)
Cite this
(In)approximability results for pattern matching problems. / Clifford, Raphaël; Popa, Alexandru.
Proceedings of the Prague Stringology Conference 2010. 2010. p. 52-62.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - (In)approximability results for pattern matching problems
AU - Clifford, Raphaël
AU - Popa, Alexandru
PY - 2010
Y1 - 2010
N2 - We consider the approximability of three recently introduced pattern matching problems which have been shown to be NP-hard. Given two strings as input, the first problem is to find the longest common parameterised subsequence between two strings. The second is a maximisation variant of generalised function matching and the third is a a maximisation variant of generalised parameterised matching. We show that in all three cases there exists an ∈ > 0 such that there is no polynomial time (1 - ∈)-approximation algorithm, unless P = NP. We then present a polynomial time √ 1/OPT-approximation algorithm for a variant of generalised parameterised matching for which no previous approximation results are known.
AB - We consider the approximability of three recently introduced pattern matching problems which have been shown to be NP-hard. Given two strings as input, the first problem is to find the longest common parameterised subsequence between two strings. The second is a maximisation variant of generalised function matching and the third is a a maximisation variant of generalised parameterised matching. We show that in all three cases there exists an ∈ > 0 such that there is no polynomial time (1 - ∈)-approximation algorithm, unless P = NP. We then present a polynomial time √ 1/OPT-approximation algorithm for a variant of generalised parameterised matching for which no previous approximation results are known.
UR - http://www.scopus.com/inward/record.url?scp=84869143041&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84869143041&partnerID=8YFLogxK
M3 - Conference contribution
SN - 9788001045978
SP - 52
EP - 62
BT - Proceedings of the Prague Stringology Conference 2010
ER -