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

Abstract

In this article 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 / 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.

Document Details

Document Type
Pub Defense Publication
Publication Date
Nov 01, 2010
Source ID
10.1145/1868237.1868249

Entities

People

  • Ke Yi
  • Lars Arge
  • Pankaj Agarwal

Organizations

  • Aarhus University
  • Army Research Office
  • Division of Environmental Biology
  • Duke University
  • Hong Kong University of Science and Technology
  • National Science Foundation
  • Research Grants Council, University Grants Committee

Tags

Fields of Study

  • Computer science
  • Mathematics

Readers

  • Computer Vision.
  • Graph Algorithms and Convex Optimization.
  • Parallel and Distributed Computing.