Towards an Optimal Space-and-Query-Time Index for Top-k Document Retrieval

preprint2012arXivOpen access

Abstract

Let $\D = ${d1,d2,...dD} \{d_1,d_2,...d_D\} be a given set of DD string documents of total length nn, our task is to index $\D$, such that the kk most relevant documents for an online query pattern PP of length pp can be retrieved efficiently. We propose an index of size ∣CSA∣+nlog⁡D(2+o(1))|CSA|+n\log D(2+o(1)) bits and O(ts(p)+klog⁡log⁡n+polylog⁡log⁡n)O(t_{s}(p)+k\log\log n+poly\log\log n) query time for the basic relevance metric \emph{term-frequency}, where ∣CSA∣|CSA| is the size (in bits) of a compressed full text index of $\D$, with O(ts(p))O(t_s(p)) time for searching a pattern of length pp . We further reduce the space to ∣CSA∣+nlog⁡D(1+o(1))|CSA|+n\log D(1+o(1)) bits, however the query time will be O(ts(p)+k(log⁡σlog⁡log⁡n)1+ε+polylog⁡log⁡n)O(t_s(p)+k(\log σ\log\log n)^{1+ε}+poly\log\log n), where σσ is the alphabet size and ε>0ε>0 is any constant.

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