A Lower Bound on Supporting Predecessor Search in k sorted Arrays

We seek to perform efficient queries for the predecessor among n values stored in k sorted arrays. Evading the Ω(n log k) lower bound from merging k arrays, we support predecessor queries in O(logn) time after O(n log( k logn )) construction time. By applying Ben-Or’s technique, we establish that this is optimal for strict predecessor queries, i.e., every data structure supporting O(logn)-time strict predecessor queries requires Ω(n log( k logn )) construction time. Our approach generalizes as a template for deriving similar lower bounds on the construction time of data structures with some desired query time.