We deal with the problem of partitioning and mapping uniform loop nests onto physical processor arrays. Resource constraints are taken into account: not only we assume a limited number of available processors, but we also assume that the communication capabilities of the physical processors are restricted (in particular, the number of communication links in each direction is bounded). This paper is motivated by the recent work of Chou and Kung and of Thiele. Our main contributions are a new formulation of the complex optimization problem to be solved in terms of a single integer linear programming problem, as well as optimal scheduling algorithms and complexity results in the case of linear processor arrays.