Path Queries on Functions

Let f : [1..n] → [1..n] be a function, and ` : [1..n] → [1..σ] indicate a label assigned to each element of the domain. We design several compact data structures that answer various queries on the labels of paths in f . For example, we can find the minimum label in f(i) for a given i and any k ≥ 0 in a given range [k1..k2], using n lgn+O(n) bits, or the minimum label in f−k(i) for given i and k > 0, using 2n lgn+O(n) bits, in time O(lgn/ lg lgn). By using n lg σ+o(n lg σ) further bits, we can also count, within the same time, the number of elements within a range of labels, and report each such element in O(1+lg σ/ lg lgn) additional time. Several other possible queries are considered, such as top-t queries and τ -majorities. Digital Object Identifier 10.4230/LIPIcs...