Faster Top-k Document Retrieval in Optimal Space

We consider the problem of retrieving the k documents from a collection of strings where a given pattern P appears most often. We show that, by representing the collection using a Compressed Suffix Array CSA, a data structure using the asymptotically optimal |CSA|+o(n) bits can answer queries in the time needed by CSA to find the suffix array interval of the pattern plus O(k lg k lg n) accesses to suffix array cells, for any constant > 0. This is lgn/ lg k times faster than the only previous solution using optimal space, lg k times slower than the fastest structure that uses twice the space, and lg k lg n times the lower-bound cost of obtaining k document identifiers from the CSA. To obtain the result we introduce a tool called the sampled document array, which can be of independent interest.