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COMPGEOM
2006
ACM

I/O-efficient batched union-find and its applications to terrain analysis

12 years 5 months ago
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...
Pankaj K. Agarwal, Lars Arge, Ke Yi
Added 20 Aug 2010
Updated 20 Aug 2010
Type Conference
Year 2006
Where COMPGEOM
Authors Pankaj K. Agarwal, Lars Arge, Ke Yi
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