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Traditional oblivious routing algorithms either do not take into account the bandwidth demand, or assume that each flow has its own private channel to guarantee deadlock freedom. Though adaptive routing schemes can react to varying network traffic, they require complicated router designs. In this thesis, we present a polynomial-time heuristic routing algorithm that takes bandwidth requirements of each flow into ac-count to minimize maximum channel load. The heuristic algorithm has two variants. The first one produces a deadlock-free route. The second one produces a minimal route, and is deadlock-free with two or more virtual channels assuming proper VC al-location. Both routing algorithms are oblivious, and need only simple router designs. The performance of each bandwidth-sensitive routing algorithm is evaluated against dimension-order routing and against the other on a number of benchmarks