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External-Memory Graph Algorithms
Chiang, Yi-Jen Goodrich, Michael T. Grove, Edward F. Tamassia, Roberto Vengroff, Darren Erik Vitter, Jeffrey Scott
Chiang, Yi-Jen
Goodrich, Michael T.
Grove, Edward F.
Tamassia, Roberto
Vengroff, Darren Erik
Vitter, Jeffrey Scott
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Abstract
We present a collection of new techniques for designing and analyzing efficient external-memory algorithms for graph problems and illustrate how these techniques can be applied to a wide variety of specific problems. Our results include:
Proximate-neighboring. We present a simple
method for deriving external-memory lower bounds
via reductions from a problem we call the “proximate neighbors” problem. We use this technique to derive non-trivial lower bounds for such problems as list ranking, expression tree evaluation, and connected components. PRAM simulation. We give methods for efficiently
simulating PRAM computations in external memory, even for some cases in which the PRAM algorithm is not work-optimal. We apply this to derive a number of optimal (and simple) external-memory graph algorithms.
Time-forward processing. We present a general
technique for evaluating circuits (or “circuit-like”
computations) in external memory. We also usethis in a deterministic list ranking algorithm.
Deterministic 3-coloring of a cycle. We give
several optimal methods for 3-coloring a cycle,
which can be used as a subroutine for finding large
independent sets for list ranking. Our ideas go
beyond a straightforward PRAM simulation, and
may be of independent interest.
External depth-first search. We discuss a method
for performing depth first search and solving related
problems efficiently in external memory. Our
technique can be used in conjunction with ideas
due to Ullman and Yannakakis in order to solve
graph problems involving closed semi-ring computations even when their assumption that vertices fit in main memory does not hold.
Our techniques apply to a number of problems, including list ranking, which we discuss in detail, finding Euler tours, expression-tree evaluation, centroid decomposition of a tree, least-common ancestors, minimum spanning tree verification, connected and biconnected components, minimum spanning forest, ear decomposition, topological sorting, reachability, graph drawing, and visibility representation.
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Date
1995
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Society for Industrial and Applied Mathematics
Research Projects
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Citation
Y.-J. Chiang, M. T. Goodrich, E. F. Grove, R. Tamassia, D. E. Vengroff, and J. S. Vitter. “External-Memory Graph Algorithms,” Proceedings of the 6th Annual SIAM/ACM Symposium on Discrete Algorithms (SODA ’95), San Francisco, CA, January 1995, 139–149.