摘要：Guruswami and Sinop give a O(1/delta) approximation guarantee for the non-uniform Sparsest Cut problem by solving O(r)-level Lasserre semidefinite constraints, provided that the generalized eigenvalues of the Laplacians of the cost and demand graphs satisfy a certain spectral condition, namely, the (r+1)-th generalized eigenvalue is at least OPT/(1-delta). Their key idea is a rounding technique that first maps a vector-valued solution to [0,1] using appropriately scaled projections onto Lasserre vectors. In this paper, we show that similar projections and analysis can be obtained using only l_2^2 triangle inequality constraints. This results in a O(r/delta^2) approximation guarantee for the non-uniform Sparsest Cut problem by adding only l_2^2 triangle inequality constraints to the usual semidefinite program, provided that the same spectral condition, the (r+1)-th generalized eigenvalue is at least OPT/(1-delta), holds.
