# Andrew Hunter

Harvey Mudd College Mathematics 2009

Final Thesis: | Locality & Complexity in Path Search |
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Thesis Proposal: | Path Search |

Talk: | Locality & Complexity in Path Search |

Poster: | Path Search |

Thesis Advisor: | Prof. Nicholas Pippenger |

Second Reader: | Prof. Ran Libeskind-Hadas |

## Locality and Complexity in Path Search

The path search problem considers a simple model of communication networks as channel graphs: directed acyclic graphs with a single source and sink. We consider each vertex to represent a switching point, and each edge a single communication line. Under a probabilistic model where each edge may independently be free (available for use) or blocked (already in use) with some constant probability, we seek to efficiently search the graph: examine (on average) as few edges as possible before determining if a path of free edge exists from source to sink. We consider the difficulty of searching various graphs under different search models, and examine the computational complexity of calculating the search cost of arbitrary graphs.