An approximation algorithm with performance guarantees for the maximum traveling salesman problem on special matrices

In this paper, we investigate the maximum traveling salesman problem (Max-TSP) on quasi-banded matrices. A matrix is quasi-banded with multiplier alpha 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 alpha 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. (C) 2002 Elsevier Science B.V. All rights reserved.