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In this paper, we present a minimum-path mapping algorithm based on genetic algorithm that automatically maps IP cores onto 2D mesh network on chip (NoC) architecture. Our algorithm consists of node mapping and minimum routing paths selection. These steps map core communication graphs onto 2D mesh NoC architectures for optimizing communication power consumption and balancing the traffic across the links under bandwidth constraint. Experimental results with several random benchmarks and a real application (a MPEG4 decoder) show that our proposed algorithm saves about 30% of power consumption compared to random mapping on average.