The present paper concentrates on one of the most common routing
models, on the Manhattan model where horizontal and vertical wire segments
are positioned on different sides of the board. While the minimum width can be
found in linear time in the single row routing, apparently there was no
efficient algorithm to find the minimum wire length. We showed before that this
problem is NP-complete in the dogleg-free case but the complexity of the
problem was still unknown in the general case. In this paper we modify the
construction applied in the former proof in order to show the NP-completeness
of routing with minimum wire length in the Manhattan model without any
restrictions
