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Abstract. Similaritysearchisafundamentalbuildingblockforinformation retrieval on a variety of datasets. The notion of a neighbor is often based on binary considerations, such as the k nearest neighbors. However, considering that data is often organized as a manifold with low intrinsic dimension, the notion of a neighbor must recognize higher-order relationship, to capture neighbors in all directions. Proximity graphs such as the Relative Neighbor Graphs (RNG), use trinary relationships which capture the notion of direc- tion and have been successfully used in a number of applications. However, the current algorithms for computing the RNG, despite widespread use, are approximate and not scalable. This paper proposes a novel type of graph, the Generalized Relative Neighborhood Graph (GRNG) for use in a pivot layer that then guides the efficient and exact construction of the RNG of a set of exemplars. It also shows how to extend this to a multi-layer hier- archy which significantly improves over the state-of-the-art methods which can only construct an approximate RNG.