Hierarchical embedding for DAG reachability queries

Abstract

Current hierarchical embeddings are inaccurate in both reconstructing the original taxonomy and answering reachability queries over Direct Acyclic Graph. In this paper, we propose a new hierarchical embedding, the Euclidean Embedding (EE), that is correct by design due to its mathematical formulation and associated lemmas. Such embedding can be constructed during the visit of a taxonomy, thus making it faster to generate if compared to other learning-based embeddings. After proposing a novel set of metrics for determining the embedding accuracy with respect to the reachability queries, we compare our proposed embedding with state-of-the-art approaches using full trees from 3 to 1555 nodes and over a real-world Direct Acyclic Graph of 1170 nodes. The benchmark shows that EE outperforms our competitors in both accuracy and efficiency.