QPF: efficient quadratic placement for FPGAs

In this paper we present QPF, a quadratic placement tool for FPGAs. Quadratic placement algorithms try to minimize total squared wire length by solving linear equations. The resulting placement tends to locate all cells near the center of the chip with a large amount of overlap. Also, since squared wire length is only an indirect measure of linear wire length, the resulting total wire length may not be minimized. We propose methods to alleviate the above two problems that give high quality results while minimizing the total run time. We incorporate multiple iterations of equation solving process together with a technique for pulling nodes out of the dense area while minimizing linear wire length. Experimental results using twenty MCNC benchmark circuits show that, on average, QPF is 5.8 times faster compared to a well known FPGA placement tool VPR, while providing almost comparable estimated total wire length.