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We present a technology mapping algorithm for implementing a random logic gate network in domino logic. The target technology of implementation is silicon-on-insulator (SOI). SOI devices exhibit an effect known as parasitic bipolar effect (PBE), which can lead to incorrect logic values in the circuit. Our algorithm solves the technology mapping problem by permitting several transformations during the mapping process in order to avoid PBE, such as transistor reordering, altering the way that transistors are organized into gates, and adding pMOS discharge transistors. We minimize the total cost of implementation, which includes discharge transistors required for correct functioning. Our algorithm generates solutions that reduce the number of discharge transistors required by 53% and reduces the size of the final solution by 6.3% on average. We compare our results with a modification of a current technology mapping algorithm for bulk CMOS domino logic that reduces the cost of the final solution and find that our algorithm outperforms this method.