### Abstract

We propose an approximation method to answer point-to-point shortest path queries in undirected edge-weighted graphs, based on random sampling and Voronoi duals. We compute a simplification of the graph by selecting nodes independently at random with probability p. Edges are generated as the Voronoi dual of the original graph, using the selected nodes as Voronoi sites. This overlay graph allows for fast computation of approximate shortest paths for general, undirected graphs. The time-quality tradeoff decision can be made at query time. We provide bounds on the approximation ratio of the path lengths as well as experimental results. The theoretical worst-case approximation ratio is bounded by a logarithmic factor. Experiments show that our approximation method based on Voronoi duals has extremely fast preprocessing time and efficiently computes reasonably short paths.

Original language | English |
---|---|

Title of host publication | Transactions on Computational Science IX - Special Issue on Voronoi Diagrams in Science and Engineering |

Pages | 28-53 |

Number of pages | 26 |

DOIs | |

Publication status | Published - 2010 Dec 13 |

Externally published | Yes |

Event | International Symposium on Voronoi Diagrams 2009 - Copenhagen, Denmark Duration: 2009 Jun 23 → 2009 Jun 26 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 6290 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | International Symposium on Voronoi Diagrams 2009 |
---|---|

Country | Denmark |

City | Copenhagen |

Period | 09/6/23 → 09/6/26 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Transactions on Computational Science IX - Special Issue on Voronoi Diagrams in Science and Engineering*(pp. 28-53). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6290 LNCS). https://doi.org/10.1007/978-3-642-16007-3_2

**Approximate shortest path queries using Voronoi duals.** / Honiden, Shinichi; Houle, Michael E.; Sommer, Christian; Wolff, Martin.

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

*Transactions on Computational Science IX - Special Issue on Voronoi Diagrams in Science and Engineering.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6290 LNCS, pp. 28-53, International Symposium on Voronoi Diagrams 2009, Copenhagen, Denmark, 09/6/23. https://doi.org/10.1007/978-3-642-16007-3_2

}

TY - GEN

T1 - Approximate shortest path queries using Voronoi duals

AU - Honiden, Shinichi

AU - Houle, Michael E.

AU - Sommer, Christian

AU - Wolff, Martin

PY - 2010/12/13

Y1 - 2010/12/13

N2 - We propose an approximation method to answer point-to-point shortest path queries in undirected edge-weighted graphs, based on random sampling and Voronoi duals. We compute a simplification of the graph by selecting nodes independently at random with probability p. Edges are generated as the Voronoi dual of the original graph, using the selected nodes as Voronoi sites. This overlay graph allows for fast computation of approximate shortest paths for general, undirected graphs. The time-quality tradeoff decision can be made at query time. We provide bounds on the approximation ratio of the path lengths as well as experimental results. The theoretical worst-case approximation ratio is bounded by a logarithmic factor. Experiments show that our approximation method based on Voronoi duals has extremely fast preprocessing time and efficiently computes reasonably short paths.

AB - We propose an approximation method to answer point-to-point shortest path queries in undirected edge-weighted graphs, based on random sampling and Voronoi duals. We compute a simplification of the graph by selecting nodes independently at random with probability p. Edges are generated as the Voronoi dual of the original graph, using the selected nodes as Voronoi sites. This overlay graph allows for fast computation of approximate shortest paths for general, undirected graphs. The time-quality tradeoff decision can be made at query time. We provide bounds on the approximation ratio of the path lengths as well as experimental results. The theoretical worst-case approximation ratio is bounded by a logarithmic factor. Experiments show that our approximation method based on Voronoi duals has extremely fast preprocessing time and efficiently computes reasonably short paths.

UR - http://www.scopus.com/inward/record.url?scp=78649807480&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649807480&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-16007-3_2

DO - 10.1007/978-3-642-16007-3_2

M3 - Conference contribution

AN - SCOPUS:78649807480

SN - 3642160069

SN - 9783642160066

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 28

EP - 53

BT - Transactions on Computational Science IX - Special Issue on Voronoi Diagrams in Science and Engineering

ER -