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)) = O(N B logM/B N B ) I/Os, where M is the memory size and B is the disk block size. This bound is asymptotically optimal in the worst case. If there are union operations that join a set with itself, our algorithm uses O(SORT(N) + MST(N)) I/Os, where MST(N) is the number of I/Os needed to compute the minimum spanning tree of a graph with N edges. We also describe a simple and practical O(SORT(N) log( N M ))-I/O algorithm for this problem, which we have implemented. We are interested in the union-find problem because of its appliin terrain analysis. A terrain can be abstracted as a height function defined...

• Type: Conference
• Year: 2006
• Where: COMPGEOM
• Authors: Pankaj K. Agarwal, Lars Arge, Ke Yi
• Keywords: Algorithms, COMPGEOM 2006, Discrete Geometry, I/o-efficient Algorithms, Union-find Problem