A 0.5358-approximation for Bandpass-2

The Bandpass-2 problem is a variant of the maximum traveling salesman problem arising from optical communication networks using wavelength-division multiplexing technology, in which the edge weights are dynamic rather than fixed. The previously best approximation algorithm for this NP-hard problem has a worst-case performance ratio of $$\frac{227}{426}.$$227426. Here we present a novel scheme to partition the edge set of a 4-matching into a number of subsets, such that the union of each of them and a given matching is an acyclic 2-matching. Such a partition result takes advantage of a known structural property of the optimal solution, leading to a $$\frac{70-\sqrt{2}}{128}\approx 0.5358$$70-2128≈0.5358-approximation algorithm for the Bandpass-2 problem.

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