### 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 use this 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.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 |

Publisher | Association for Computing Machinery |

Pages | 139-149 |

Number of pages | 11 |

Volume | Part F129524 |

ISBN (Electronic) | 0898713498 |

State | Published - Jan 22 1995 |

Event | 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 - San Francisco, United States Duration: Jan 22 1995 → Jan 24 1995 |

### Other

Other | 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 |
---|---|

Country | United States |

City | San Francisco |

Period | 1/22/95 → 1/24/95 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995*(Vol. Part F129524, pp. 139-149). Association for Computing Machinery.

**External-memory graph algorithms.** / Chiang, Yi-Jen; Goodrich, Michael T.; Grove, Edward F.; Tamassia, Roberto; Vengroff, Darren Erik; Vitter, Jeffrey Scott.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995.*vol. Part F129524, Association for Computing Machinery, pp. 139-149, 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995, San Francisco, United States, 1/22/95.

}

TY - GEN

T1 - External-memory graph algorithms

AU - Chiang, Yi-Jen

AU - Goodrich, Michael T.

AU - Grove, Edward F.

AU - Tamassia, Roberto

AU - Vengroff, Darren Erik

AU - Vitter, Jeffrey Scott

PY - 1995/1/22

Y1 - 1995/1/22

N2 - 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 use this 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.

AB - 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 use this 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.

UR - http://www.scopus.com/inward/record.url?scp=84994666437&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994666437&partnerID=8YFLogxK

M3 - Conference contribution

VL - Part F129524

SP - 139

EP - 149

BT - Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995

PB - Association for Computing Machinery

ER -