Wavefront and caustic surfaces of refractive laser beam shaper
David L. Shealy, John A. Hoffnagle
SPIE Optical Engineering + Applications 2007
We consider the well-known minimum quadratic assignment problem. In this problem we are given two n × n nonnegative symmetric matrices A = (a ij) and B = (bij). The objective is to compute a permutation π of V = {1,⋯,n} so that ∑ i,jεVi≠j aπ(i),π(j)bi,j is minimized. We assume that A is a 0/1 incidence matrix of a graph, and that B satisfies the triangle inequality. We analyze the approximability of this class of problems by providing polynomial bounded approximations for some special cases, and inapproximability results for other cases. © 2009 ACM.
David L. Shealy, John A. Hoffnagle
SPIE Optical Engineering + Applications 2007
Michael E. Henderson
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
M. Tismenetsky
International Journal of Computer Mathematics
Michael Ray, Yves C. Martin
Proceedings of SPIE - The International Society for Optical Engineering