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註釋Abstract: "Network throughput can be increased by allowing multipath, adaptive routing. Adaptive routing allows more freedom in the paths taken by messages, spreading load over physical channels more evenly. The flexibility of adaptive routing introduces new possibilities of deadlock. Previous deadlock avoidance schemes in k-ary n-cubes require an exponential number of virtual channels [1]. We describe a family of deadlock-free routing algorithms, called planar-adaptive routing algorithms which require only a constant number of virtual channels, independent of network size and dimension.