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 configurahle multiprocessors. This new routing problem poses interesting algorithmic problems. In a previous paper of IEEE TRANSACTION ON COMPUTER-AIDED DESIGN, the study of the complexity of segmented channel routing WBS 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 El Gamal, Greene, and Roychowdhury.