Computation over APT compressed data

The Arithmetic Progressions Tree (APT) is a data structure storing an encoding of a monotonic sequence L in [1.n]. Previous work on APTs focused on its theoretical and experimental compression guarantees. This paper is the first to consider computations over APT compressed data. In particular: 1. We show how to perform a search for any sub-sequence/a set of the monotone sequence L in time proportional to the query sub-sequence length/set size multiplied by the size of the APT compressed representation of L. 2. We show how, given the APT compressed representation of the monotone sequence L, we can find a minimum run-length of L in constant time, a maximum run-length of L in O(logn) time, and all runs of L in constant time plus the output size. 3. We show how, given the APT compressed representation of the monotone sequence L, we can answer whether a consecutive periodic pattern P is represented by an APT-node in O(logn) time and report occurrences of P in L within the processing time of the output size. 4. In addition, we improve the APT construction algorithm time and space complexity.