● If both additions and subtractions are allowed, then the problem requires Q(n log log n) arithmetic operations. This is the first general result for the group model. Note, however, that it falls short of the best known upper bound of O(n log n). The proof uses the spectral method of [5]. This reduces the problem to that of finding a set system A such that the eigenvalues of ATA are large. We do this nonconstructively by using a mixture of algebraic and probabilistic arguments. The key… CONTINUE READING