Succinct Indices for Range Queries with Applications to Orthogonal Range Maxima

We consider the problem of preprocessing N points in 2D, each endowed with a priority, to answer the following queries: given a axis-parallel rectangle, determine the point with the largest priority in the rectangle. Using the ideas of the effective entropy of range maxima queries and succinct indices for range maxima queries, we obtain a structure that uses O(N) words and answers the above query in O(lgN lg lgN) time. This is a direct improvement of Chazelle’s result from 1985 [11] for this problem – Chazelle required O(N/ ) words to answer queries in O((lgN) ) time for any constant > 0.