• An earlier proof of NP-completeness of the IPF problem on 3D lattices [W.E. Hart, On the computational complexity of sequence design problems, Proceedings of the First Annual International Conference on Computational Molecular Biology 1997, pp. 128–136] is based on the NP-completeness of the IPF problem on the 2D lattices. However, the reduction was not correct and we show that the IPF problem for 2D lattices can be solved in O(K|V|) time. But, we show that the IPF problem on 3D lattices is indeed NP-complete by a providing a different reduction from a different NP-complete problem.
• We design a polynomial-time approximation scheme for the IPF problem on 3D lattices using the shifted slice-and-dice approach in [P. Berman, B. DasGupta, S. Muthukrishnan, Approximation algorithms for MAX-MIN tiling, J. Algorithms 47(2) (2003) 122–134; D. Hochbaum, Approximation Algorithms for NP-hard Problems, PWS Publishing Company, MA, 1997; D.S. Hochbaum, W. Mass, Approximation schemes for covering and packing problems in image processing and VLSI, J. ACM 32(1) (1985) 130–136], thereby improving the previous best polynomial-time approximation algorithm which had a performance ratio of [W.E. Hart, On the computational complexity of sequence design problems, Proceedings of the First Annual International Conference on Computational Molecular Biology 1997, pp. 128–136].