  Many applications require efficient management of large sets of intervals
because many objects are associated with intervals (e.g., time and price
intervals). In such interval management systems, range search is a primitive
operator for retrieving and analysis tasks. As dataset sizes are growing
nowadays, range search results are also becoming larger, which may overwhelm
users and incur long computation time. Because applications are usually
satisfied with a subset of the result set, it is desirable to efficiently
obtain only small samples from the result set.We therefore address the problem
of independent range sampling on interval data, which outputs $s$ random
samples that overlap a given query interval and are independent of the samples
of all previous queries. To efficiently solve this problem theoretically and
practically, we propose a variant of an interval tree, namely the augmented
interval tree (or AIT), and we show that there exists an exact algorithm that
needs $O(n \log n)$ space and $O(\log^{2} n + s)$ time, where $n$ is the
dataset size. The simple structure of an AIT provides flexible extensions: (i)
its time and space complexities respectively become $O(\log^{2} n + s)$
expected and $O(n)$ by bucketing intervals and (ii) it can deal with weighted
intervals and outputs $s$ weighted random samples in $O(\log^{2} n+s\log n)$
time. We conduct extensive experiments on real datasets, and the results
demonstrate that our algorithms significantly outperform competitors.
