### Abstract

In this paper we study several routing problems that generalize shortest paths and the Traveling Salesman Problem. We consider a more general model that incorporates the actual cost in terms of gas prices. We have a vehicle with a given tank capacity. We assume that at each vertex gas may be purchased at a certain price. The objective is to find the cheapest route to go from s to t, or the cheapest tour visiting a given set of locations. Surprisingly, the problem of find the cheapest way to go from s to t can be solved in polynomial time and is not NP-complete. For most other versions however, the problem is NP-complete and we develop polynomial time approximation algorithms for these versions.

Original language | English (US) |
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Title of host publication | Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings |

Pages | 534-545 |

Number of pages | 12 |

State | Published - Dec 1 2007 |

Event | 15th Annual European Symposium on Algorithms, ESA 2007 - Eilat, Israel Duration: Oct 8 2007 → Oct 10 2007 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4698 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 15th Annual European Symposium on Algorithms, ESA 2007 |
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Country | Israel |

City | Eilat |

Period | 10/8/07 → 10/10/07 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings*(pp. 534-545). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4698 LNCS).