### Abstract

We describe a procedure which may be helpful to any disorganized carpenter who has a mixed pile of bolts and nuts and wants to find the corresponding pairs of bolts and nuts. The procedure uses our (and the carpenter's) ability to construct efficiently highly expanding graphs. The problem considered is given a collection of n bolts of distinct widths and n nuts such that there is a 1-1 correspondence between the nuts and bolts. The goal is to find for each bolt its corresponding nut by comparing nuts to bolts but not nuts to nuts or bolts to bolts. Our objective is to minimize the number of operations of this kind (as well as the total running time). The problem has a randomized algorithm similar to Quicksort. Our main result is an n(log n)^{O(1)}-time deterministic algorithm, based on expander graphs, for matching the bolts and the nuts.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms |

Publisher | Publ by ACM |

Pages | 690-696 |

Number of pages | 7 |

ISBN (Print) | 0898713293 |

State | Published - Jan 1 1994 |

Externally published | Yes |

Event | Proceedings of the Fifth Annual SIAM Symposium on Discrete Algorithms - Arlington, VA, USA Duration: Jan 23 1994 → Jan 25 1994 |

### Other

Other | Proceedings of the Fifth Annual SIAM Symposium on Discrete Algorithms |
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City | Arlington, VA, USA |

Period | 1/23/94 → 1/25/94 |

### All Science Journal Classification (ASJC) codes

- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality
- Discrete Mathematics and Combinatorics

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## Cite this

*Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms*(pp. 690-696). Publ by ACM.