Publication Date:
2016-05-28
Description:
Let \(\mathcal {D} = \{\mathsf {T}_1,\mathsf {T}_2, \ldots ,\mathsf {T}_D\}\) 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 \((P[1\ldots p],k)\) , 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.
Print ISSN:
0178-4617
Electronic ISSN:
1432-0541
Topics:
Computer Science
,
Mathematics
