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Approximate nearest neighbor search (ANNS) is a key retrieval technique for vector database and many data center applications, such as person re-identification and recommendation systems. It is also fundamental to retrieval augmented generation (RAG) for large language models (LLM) now. Among all the ANNS algorithms, graph-traversal-based ANNS achieves the highest recall rate. However, as the size of dataset increases, the graph may require hundreds of gigabytes of memory, exceeding the main memory capacity of a single workstation node. Although we can do partitioning and use solid-state drive (SSD) as the backing storage, the limited SSD I/O bandwidth severely degrades the performance of the system. To address this challenge, we present NDSEARCh, a hardware-software co-designed near-data processing (NDP) solution for ANNS processing. NDSeARCH consists of a novel in-storage computing architecture, namely, SEARSSD, that supports the ANNS kernels and leverages logic unit (LUN)-level parallelism inside the NAND flash chips. NDSEARCH also includes a processing model that is customized for NDP and cooperates with SearSSD. The processing model enables us to apply a two-level scheduling to improve the data locality and exploit the internal bandwidth in NDSearch, and a speculative searching mechanism to further accelerate the ANNS workload. Our results show that NDSEARCH improves the throughput by up to 31.7×,14.6×,7.4×, and 2.9× over CPU, GPU, a state-of-the-art SmartSSD-only design, and DeepStore, respectively. NDSEARCH also achieves two orders-of-magnitude higher energy efficiency than CPU and GPU.