Dynamic top-k range reporting in external memory

Abstract

In the top-K range reporting problem, the dataset contains N points in the real domain ℜ, each of which is associated with a real-valued score. Given an interval x₁,x₂ in ℜ and an integer K≤ N, a query returns the K points in x₁,x₂ having the smallest scores. We want to store the dataset in a structure so that queries can be answered efficiently. In the external memory model, the state of the art is a static structure that consumes O(N/B) space, answers a query in O(log_B N + K/B) time, and can be constructed in O(N + (N log N / B) log _M/B (N/B)) time, where B is the size of a disk block, and M the size of memory. We present a fully-dynamic structure that retains the same space and query bounds, and can be updated in O(log²_B N) amortized time per insertion and deletion. Our structure can be constructed in O((N/B) log _M/B (N/B)) time.