I/O-Efficient Batched Union-Find and Its Applications to Terrain Analysis

Despite extensive study over the last four decades and numerous applications, no I/O-efficient algorithm is known for the union-find problem. In this paper we present an I/O-efficient algorithm for the batched (off-line) version of the union-find problem. Given any sequence of N union and find operations, where each union operation joins two distinct sets, our algorithm uses O(SORT(N))