アイテム詳細

要旨

In this paper we consider various encoding problems for range queries on arrays. In these problems, the goal is that the encoding occupies the information theoretic minimum space required to answer a particular set of range queries. Given an array $A[1..n]$ a range top-$k$ query on an arbitrary range $[i,j] \subseteq [1,n]$ asks us to return the ordered set of indices $\{l_1 ,...,l_k \}$ such that $A[l_m]$ is the $m$-th largest element in $A[i..j]$. We present optimal encodings for range top-$k$ queries, as well as for a new problem which we call range min-max, in which the goal is to return the indices of both the minimum and maximum element in a range.