Abstract
Given a pattern p over an alphabet Σ p and a text t over an alphabet Σ t , we consider the problem of determining a mapping f from Σ p to \({\Sigma}_{t}^{+}\) such that t = f(p 1)f(p 2)...f(p m ). This class of problems, which was first introduced by Amir and Nor in 2004, is defined by different constraints on the mapping f. We give NP-Completeness results for a wide range of conditions. These include when f is either many-to-one or one-to-one, when Σ t is binary and when the range of f is limited to strings of constant length. We then introduce a related problem we term pattern matching with string classes which we show to be solvable efficiently. Finally, we discuss an optimisation variant of generalised matching and give a polynomial-time min \((1,\sqrt{k/OPT})\)-approximation algorithm for fixed k.
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References
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Clifford, R., Harrow, A.W., Popa, A., Sach, B. (2009). Generalised Matching. In: Karlgren, J., Tarhio, J., Hyyrö, H. (eds) String Processing and Information Retrieval. SPIRE 2009. Lecture Notes in Computer Science, vol 5721. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03784-9_29
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DOI: https://doi.org/10.1007/978-3-642-03784-9_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03783-2
Online ISBN: 978-3-642-03784-9
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