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We consider the problem of preprocessing $N$ points in 2D, each endowed witha priority, to answer the following queries: given a axis-parallel rectangle,determine the point with the largest priority in the rectangle. Using the ideasof the \emph{effective entropy} of range maxima queries and \emph{succinctindices} for range maxima queries, we obtain a structure that uses O(N) wordsand answers the above query in $O(\log N \log \log N)$ time. This is a directimprovement of Chazelle's result from FOCS 1985 for this problem -- Chazellerequired $O(N/\epsilon)$ words to answer queries in $O((\log N)^{1+\epsilon})$time for any constant $\epsilon > 0$.

Succinct Indices for Range Queries with applications to Orthogonal Range Maxima