A more efficient algorithm to compute the Rand Index for change-point problems

We provide a more efficient algorithm for computing the Rand Index when the data cluster comes from a change-point detection problem. Given $N$ data points and two clusterings of size $r$ and $s$, the algorithm runs on $O(r+s)$ time complexity and $O(1)$ memory complexity. The traditional algorithm, in contrast, runs on $O(rs+N)$ time complexity and $O(rs)$ memory complexity.