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We study the Korteweg-de Vries equation posed on the quarter plane with asymptotically t-periodic boundary data for large t > 0. We derive an expression for the Dirichlet to Neumann map to all orders in the perturbative expansion of a small ϵ > 0 in the case of the asymptotically periodic boundary data. More precisely, we show that if the unknown Neumann boundary data are asymptotically periodic for large t in the sense that u x ( 0 , t ) and u x x ( 0 , t ) tend to periodic functions g ˜ 1 ( t ) and g ˜ 2 ( t ) for large t, respectively, then the periodic functions g ˜ 1 ( t ) and g ˜ 2 ( t ) can be characterized in terms of the given asymptotically periodic Dirichlet boundary datum u ( 0 , t ). Moreover, we determine effectively the Fourier coefficients of the functions g ˜ 1 ( t ) and g ˜ 2 ( t ) by solving a certain recursive algebraic equations. [ABSTRACT FROM AUTHOR]