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DNA sequencing is the physical/biochemical process of identifying the location of the four bases (Adenine, Guanine, Cytosine, Thymine) in a DNA strand. As semiconductor technology revolutionized computing, modern DNA sequencing technology (termed Next Generation Sequencing, NGS) revolutionized genomic research. As a result, modern NGS platforms can sequence hundreds of millions of short DNA fragments in parallel. The sequenced DNA fragments, representing the output of NGS platforms, are termed reads. Besides genomic variations, NGS imperfections induce noise in reads. Mapping each read to (the most similar portion of) a reference genome of the same species, i.e., read mapping, is a common critical first step in a diverse set of emerging bioinformatics applications. Mapping represents a search-heavy memory-intensive similarity matching problem, therefore, can greatly benefit from near-memory processing. Intuition suggests using fast associative search enabled by Ternary Content Addressable Memory (TCAM) by construction. However, the excessive energy consumption and lack of support for similarity matching (under NGS and genomic variation induced noise) renders direct application of TCAM infeasible, irrespective of volatility, where only non-volatile TCAM can accommodate the large memory footprint in an area-efficient way. This paper introduces GeNVoM, a scalable, energy-efficient and high-throughput solution. Instead of optimizing an algorithm developed for general-purpose computers or GPUs, GeNVoM rethinks the algorithm and non-volatile TCAM-based accelerator design together from the ground up. Thereby GeNVoM can improve the throughput by up to 3.67×; the energy consumption, by up to 1.36×, when compared to an ASIC baseline, which represents one of the highest-throughput implementations known.