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Recent DNA pre-alignment filter designs employ DRAM for storing the reference genome and its associated meta-data. However, DRAM incurs increasingly high energy consumption background and refresh energy as devices scale. To overcome this problem, this paper explores a design with racetrack memory (RTM)--an emerging non-volatile memory that promises higher storage density, faster access latency, and lower energy consumption. Multi-bit storage cells in RTM are inherently sequential and thus require data placement strategies to mitigate the performance and energy impacts of shifting during data accesses. We propose a near-memory pre-alignment filter with a novel data mapping and several shift reduction strategies designed explicitly for RTM. On a set of four input genomes from the 1000 Genome Project, our approach improves performance and energy efficiency by 68% and 52%, respectively, compared to the state of the art proposed DRAM-based architecture.