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Top-$$k$$ term-proximity in succinct space. (English) Zbl 1370.68075
Summary: Let $$\mathcal {D} = \{\mathsf {T}_1,\mathsf {T}_2,\dotsc,\mathsf {T}_D\}$$ be a collection of $$D$$ string documents of $$n$$ characters in total, that are drawn from an alphabet set $$\varSigma =[\sigma ]$$. The top-k document retrieval problem is to preprocess $$\mathcal{D}$$ into a data structure that, given a query $$(P[1\dotsc p],k)$$, can return the $$k$$ documents of $$\mathcal{D}$$ most relevant to the pattern $$P$$. The relevance is captured using a predefined ranking function, which depends on the set of occurrences of $$P$$ in $$\mathsf {T}_d$$. For example, it can be the term frequency (i.e., the number of occurrences of $$P$$ in $$\mathsf {T}_d$$), or it can be the term proximity (i.e., the distance between the closest pair of occurrences of $$P$$ in $$\mathsf {T}_d$$), or a pattern-independent importance score of $$\mathsf {T}_d$$ such as PageRank. Linear space and optimal query time solutions already exist for the general top-$$k$$ document retrieval problem. Compressed and compact space solutions are also known, but only for a few ranking functions such as term frequency and importance. However, space efficient data structures for term proximity based retrieval have been evasive. In this paper we present the first sub-linear space data structure for this relevance function, which uses only $$o(n)$$ bits on top of any compressed suffix array of $$\mathcal{D}$$ and solves queries in $$O((p+k)\, {{\mathrm{polylog}}}\;n)$$ time. We also show that scores that consist of a weighted combination of term proximity, term frequency, and document importance, can be handled using twice the space required to represent the text collection.

##### MSC:
 68P20 Information storage and retrieval of data 68P05 Data structures
Wumpus
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