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The single-row routing approach for layout has attracted a great deal of interest and is in a position to become one of the fundamental routing methods for high density multilayer printed wiring boards (PWB's). A specific development has recently been accomplished on this approach , namely: Necessary and sufficient conditions for optimum routing have been obtained. Nonetheless, there still remains a fundamental problem to be overcome, that is, to develop an algorithm to find the optimum solution. The present paper derives an alternate set of necessary and sufficient conditions for the same problem. These are easy to check and are tailored for algorithm development. An efficient algorithm in the special cases of upper and lower street congestions up to two has been proposed. These special cases are particularly of interest in the design of practical PWB's.