Abstract Pattern Matching Using n-Gram Sampling of Cumulative Algebraic Signatures: Preliminary Results

We propose a novel string (pattern) matching algorithm called n-gram search. We intend it for the records stored once and searched many times in a database or a file, especially those organized in a Scalable Distributed Data Structure, (SDDS), over a grid or a structured P2P net. We presume that the records are encoded into their cumulative algebraic signatures, providing incidental confidentiality of stored data. The search starts with pre-processing the pattern, calculating the logarithmic algebraic signature (LAS) of the pattern and the LASs of every n-gram in it. The value of n ≥ 1 is a parameter that one may tune. The search attempts to match the LASs of n-grams in the pattern towards dynamically calculated LASs, sampled over n-grams in the records. A mismatch generates a shift of up to K-n symbols towards next sample, where K is the pattern length. The whole process is parallel over the SDDS servers and does not require any local decoding. For an M-symbol long record, the unsuccessful search, measured as number of match attempts, costs O ((M-K) / (Kn+1)). The 2-grams should typically suffice, leading to O ((M-K) / (K-1)). We show that the algorithm particularly efficient for larger strings and records, i.e., with e-documents or DNA data. Preliminary results show then the n-gram search about (K- n + 1) faster than our previous algorithms and among the fastest known, e.g., probably often faster than Boyer-Moore