### Abstract

We propose an approximation method to answer point-to-point shortest path queries in undirected 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 |
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Title of host publication | 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009 |

Pages | 53-62 |

Number of pages | 10 |

DOIs | |

Publication status | Published - 2009 Dec 1 |

Externally published | Yes |

Event | 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009 - Copenhagen, Denmark Duration: 2009 Jun 23 → 2009 Jun 26 |

### Other

Other | 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009 |
---|---|

Country | Denmark |

City | Copenhagen |

Period | 09/6/23 → 09/6/26 |

### Fingerprint

### Keywords

- Approximation
- Distance oracle
- Graph Voronoi diagram
- Shortest path

### ASJC Scopus subject areas

- Information Systems
- Biomedical Engineering
- Applied Mathematics

### Cite this

*6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009*(pp. 53-62). [5362417] https://doi.org/10.1109/ISVD.2009.30

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

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

*6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009.*, 5362417, pp. 53-62, 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009, Copenhagen, Denmark, 09/6/23. https://doi.org/10.1109/ISVD.2009.30

}

TY - GEN

T1 - Approximate shortest path queries in graphs using Voronoi duals

AU - Honiden, Shinichi

AU - Houle, Michael E.

AU - Sommer, Christian

AU - Wolff, Martin

PY - 2009/12/1

Y1 - 2009/12/1

N2 - We propose an approximation method to answer point-to-point shortest path queries in undirected 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 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.

KW - Approximation

KW - Distance oracle

KW - Graph Voronoi diagram

KW - Shortest path

UR - http://www.scopus.com/inward/record.url?scp=77951493159&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951493159&partnerID=8YFLogxK

U2 - 10.1109/ISVD.2009.30

DO - 10.1109/ISVD.2009.30

M3 - Conference contribution

SN - 9780769537818

SP - 53

EP - 62

BT - 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009

ER -