An approximation algorithm for the Bandpass-2 problem

The general Bandpass-$B$ problem is NP-hard and can be approximated by a reduction into the weighted $B$-set packing problem, with a worst case performance ratio of $O(B^2)$. When $B = 2$, a maximum weight matching gives a 2-approximation to the problem. In this paper, we call the Bandpass-2 problem simply the Bandpass problem. The Bandpass problem can be viewed as a variation of the maximum traveling salesman problem, in which the edge weights are dynamic rather than given at the front. We present a ${426}{227}$-approximation algorithm for the problem. Such an improved approximation is built on an intrinsic structural property proven for the optimal solution and several novel schemes to partition a $b$-matching into desired matchings.