## Abstract

We consider a special traveling salesman problem (TSP) called bi-weighted TSP. The problem of determining an optimal ordering for a set of parallel wires to minimize crosstalk noise can be formulated as a bi-weighted TSP problem. Let G be an undirected complete weighted graph where the weight (cost) on each edge is either 1 or 1 + α. The objective of the bi-weighted TSP problem is to find a minimum cost Hamiltonian path in G. Existing algorithms for general TSP (e.g., nearest-neighbor algorithm and Christofide algorithm) can be applied to solve this problem. In this paper, we prove that the nearest-neighbor algorithm has worst case performance ratio of 1 + α/2 and the bound is tight. We also show that the algorithm is asymptotically optimal when m is o(n^{2}), where n is the number of nodes in G and m is the number of edges with cost 1 + α. Analysis of the Christofide algorithm will also be presented.

Original language | English (US) |
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Pages (from-to) | III/767-III/770 |

Journal | Proceedings - IEEE International Symposium on Circuits and Systems |

Volume | 3 |

State | Published - 2002 |

Externally published | Yes |

Event | 2002 IEEE International Symposium on Circuits and Systems - Phoenix, AZ, United States Duration: May 26 2002 → May 29 2002 |

## ASJC Scopus subject areas

- Electrical and Electronic Engineering