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

I/O-efficient batched union-find and its applications to terrain analysis (2006)

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by Pankaj K. Agarwal Lars Arge , Ke Yi

Venue:	In Proc. 22nd Annual Symposium on Computational Geometry
Citations:	14 - 8 self

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Datum	Value	Source
TITLE	I/O-efficient batched union-find and its applications to terrain analysis	INFERENCE
AUTHOR NAME	Pankaj K. Agarwal Lars Arge	SVM HeaderParse 0.2
AUTHOR AFFIL	1 Department of Computer Science, Duke University	SVM HeaderParse 0.2
AUTHOR ADDR	Durham, NC 27708, USA.	SVM HeaderParse 0.2
AUTHOR NAME	Ke Yi	SVM HeaderParse 0.2
AUTHOR AFFIL	1 Department of Computer Science, Duke University	SVM HeaderParse 0.2
AUTHOR ADDR	Durham, NC 27708, USA.	SVM HeaderParse 0.2
ABSTRACT	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 log M/B N 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 applications in terrain analysis. A terrain can be abstracted as a height function defined over R2, and many problems that deal with such functions require a union-find data structure. With the emergence of modern mapping technologies, huge amount of elevation data is being generated that is too large to fit in memory, thus I/O-efficient algorithms are needed to process this data efficiently. In this paper, we study two terrain-analysis problems that benefit from a union-find data structure: (i) computing topological persistence and (ii) constructing the contour tree. We give the first O(SORT(N))-I/O algorithms for these two problems, assuming that the input terrain is represented as a triangular mesh with N vertices. Finally, we report some preliminary experimental results, showing that our algorithms give order-ofmagnitude improvement over previous methods on large data sets that do not fit in memory. 1	SVM HeaderParse 0.2
YEAR	2006	INFERENCE
VENUE	In Proc. 22nd Annual Symposium on Computational Geometry	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	167--176	INFERENCE
VOLUME	2006	INFERENCE
CITATIONS	36 found	ParsCit 1.0