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As the level of chip-integration continues to advance at a fast pace, the desire for efficient interconnects - whether on-chip or off-chip - is rapidly increasing. Traditional interconnects like buses, point-to-point wires, and regular topologies may suffer from poor resource sharing in the time and space domains, leading to high contention or low resource utilization. In this paper, we propose a design methodology for constructing networks for special-purpose computer systems with well-behaved (known) communication characteristics. A temporal and spatial model is proposed to define the sufficient condition for contention-free communication. Based upon this model, a design methodology using a recursive bisection technique is applied to systematically partition a parallel system such that the required number of links and switches is minimized while achieving low contention. Results show that the design methodology can generate more optimized on-chip networks with up to 60 percent fewer resources than meshes or tori while providing blocking performance closer to that of a fully connected crossbar.