Generalised Matching

Given a pattern p over an alphabet Σp and a text t over an alphabet Σt, we consider the problem of determining a mapping f from Σp to Σ+ t such that t = f(p1)f(p2) . . . f(pm). 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-toone or one-to-one, when Σt 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, p k/OPT)-approximation algorithm for fixed k.

• Type: Conference
• Year: 2009
• Where: SPIRE
• Authors: Raphaël Clifford, Aram Wettroth Harrow, Alexandru Popa, Benjamin Sach
• Keywords: Alphabet Σp, Alphabet Σt, Information Retrieval, Mapping F, SPIRE 2009