## Abstract

In this paper, we investigate the maximum traveling salesman problem (Max-TSP) on quasi-banded matrices. A matrix is quasi-banded with multiplier α if all its elements contained within a band of several diagonals above and below the principal diagonal are non-zero, and any element in the band is at least α times larger than the maximal element outside the band. We investigate the properties of the Max-TSP on the quasi-banded matrices, prove that it is strongly NP-hard and derive a linear-time approximation algorithm with a guaranteed performance.

Original language | English |
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Pages (from-to) | 139-148 |

Number of pages | 10 |

Journal | Discrete Applied Mathematics |

Volume | 119 |

Issue number | 1-2 |

DOIs | |

State | Published - 15 Jun 2002 |

Externally published | Yes |

### Bibliographical note

Funding Information:This research was supported in part by INTAS Grant no. 96-0812 and Grant no. 8951-2-98 from the Ministry of Science of Israel. Valuable comments and criticisms from two anonymous referees are gratefully acknowledged.

### Funding

This research was supported in part by INTAS Grant no. 96-0812 and Grant no. 8951-2-98 from the Ministry of Science of Israel. Valuable comments and criticisms from two anonymous referees are gratefully acknowledged.

Funders | Funder number |
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INTAS | 96-0812, 8951-2-98 |

Ministry of Science of Israel |

## Keywords

- Approximation algorithms with performance guarantees
- Banded matrices
- Maximum traveling salesman problem
- Polynomial algorithm