The bi-weighted TSP problem for VLSI crosstalk minimization

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(n²), 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.