Top-k Term-Proximity in Succinct Space

Ian Munro, Gonzalo Navarro, Jesper Sindahl Nielsen, Rahul Shah, and Sharma Thankachan

Let DD = {T_1,T_2,...T_D} be a collection of D string documents of n characters in total, that are drawn from an alphabet set S=[s]. The top-k document retrieval problem is to preprocess DD into a data structure that, given a query (P[1..p],k), can return the k documents of DD most relevant to pattern P. The relevance is captured using a predefined ranking function, which depends on the set of occurrences of P in T_d. For example, it can be the term frequency (i.e., the number of occurrences of P in T_d), or it can be the term proximity (i.e., the distance between the closest pair of occurrences of P in T_d), or a pattern-independent importance score of T_d such as PageRank. Linear space and optimal query time solutions already exist for this 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 DD and solves queries in time O((p+k) polylog n).