The complexity of segmented channel routing

The segmented channel routing problem arises in the wiring and the physical design automation for Field Programmable Gate Arrays (FPGA´s), a new type of electrically programmable VLSI. It may also be applicable to configurable multiprocessors. This new routing problem poses interesting algorithmic problems. In a previous paper by V. P. Roychowdhury et al. (see ibid., vol.12, no. 1, p. 79-95, 1993), the study of the complexity of segmented channel routing was reported. In this paper, we point out that the strong NP-completeness proof of segmented channel routing in that previous paper is incomplete and incorrect. We provide a correct proof which shows that the problem is indeed NP-complete in the strong sense and, therefore, that an exact polynomial time algorithm for the general case of the problem does not exist unless P=NP. Since our construction also holds for the case where connection lengths are bounded by a constant, we then settle an open question raised by Roychowdhury et al