Hashing and indexing: Succinct data structures and smoothed analysis

Abstract

© Springer International Publishing Switzerland 2014.We consider the problem of indexing a text T (of length n) with a light data structure that supports efficient search of patterns P (of length m) allowing errors under the Hamming distance. We propose a hash-based strategy that employs two classes of hash functions—dubbed Hamming-aware and de Bruijn—to drastically reduce search space and memory footprint of the index, respectively. We use our succinct hash data structure to solve the k-mismatch search problem in 2n log σ + o(n log σ) bits of space with a randomized algorithm having smoothed complexity (Formula presented.), where σ is the alphabet size, occ is the number of occurrences, and ξ is a term depending on m, n, and on the amplitude ε of the noise perturbing text and pattern. Significantly, we obtain that for any ε > 0, for m large enough, ξ ∈ O(log m): our results improve upon previous linear-space solutions of the k-mismatch problem.

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Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
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