  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.
