There are various strategies of reducing computational costs by using more compact representations of many-body wave-functions and the Hamiltonian. The sparsity of twoelectron repulsion integrals (ERI) can be utilized through the approximate decomposition over auxiliary basis sets obtained by density fitting, as in the resolution-of-identity (RI) methods , or by Cholesky decomposition of ERIs , or using alternative schemes such as pseudospectral decomposition , chain-of-spheres exchange , and tensor hypercontraction . Decomposition of ampliomtudes can also be used to reduce computational costs . A number of strategies exploit the physical decay of Coulomb interaction with a distance by using localized orbitals . Based on orbital localization and truncation of non-interacting orbital subsets, reduced-scaling versions of MP2 , CCSD , (T) correction and beyond have been developed.