Summary: We apply the recently developed theory of information-based complexity to two-dimensional transport [cf. the authors, ibid. 21, No. 3, 237-257 (1992; Zbl 0756.65154)]. For a model problem we obtain the radius of the cell-average information, which is the optimal (worst-case) error. The corresponding central algorithm that possesses this optimal error is developed. Further, we theoretically and numerically compare four algorithms, the step-characteristic, diamond-difference, $(C,C)$ nodal-transport, and corner-balance algorithms, for a single cell. A number of figures and tables are presented for those comparisons. Such results allow the best choice of algorithm to solve the model problem, depending on the angular variables ($μ,η$) and the cell width $h$.