On spatial keyword covering

This article introduces and solves a spatial keyword cover problem ( SK-Cover for short), which aims to identify the group of spatio-textual objects covering all the keywords in a query and minimizing a distance cost function that leads to fewer objects in the answer set. In a broad sense, SK-Cover has been actively studied in the literature of spatial keyword search , such as the m -closest keywords query and the collective spatial keyword query . However, these existing works focus on minimizing only the largest pairwise distance even though the actual spatial cost is highly influenced by the number of objects in the answer group. Motivated by this, the present article further generalizes the problem definition in such a way that the total cost takes the cardinality of the group as well as the spatial distance. We prove that SK-Cover is not only NP-hard but also does not allow an approximation better than O(log|T|) in polynomial time, where T is the set of query keywords. We first establish an O(log|T|) -approximation algorithm, which is asymptotically optimal in terms of the approximability of SK-Cover , together with effective accessing strategies and pruning rules to improve the overall efficiency and scalability. Despite the NP-hardness of SK-Cover , this article also develops exact solutions that find the optimal group of objects in a reasonably fast manner in practice, especially when it is required to cover a relatively small number of query keywords. In addition to our algorithmic results, we empirically show that our approximation algorithm always achieves the best accuracy and the efficiency comparable to that of a state-of-the-art algorithm intended for mCK , a problem similar to yet theoretically easier than SK-Cover , and also demonstrate that our exact algorithm using the proposed approximation scheme runs much faster than the baseline algorithm adapted from the existing solution for mCK .