Unit integer quadratic binary programming

This paper presents an efficient method of computing $\text{?′}{}_{\mathrm{<mtext>max</mtext>}}\text{=}\text{max}\text{Y}\text{Y}{}^{\mathrm{<mtext>T</mtext>}}\text{AY}$, where Y is an N-dimensional vector of ±1 entries and A is a real symmetric matrix. The ratio of number of computations required by this method to that by the direct method is approximately ($\text{3}\text{2N}$), where the direct method corresponds to computing Y^TAY for all possible Y and then finding the maximum from these. This problem has important applications in operations research, matrix theory, signal processing, communication theory, control theory, and others. Some of these are discussed in this paper.