Christopher Musco @ Theory Lunch скачать в хорошем качестве

Christopher Musco @ Theory Lunch

Title: Navigability and Graph-based Vector Search Abstract: In the last few years, we have seen a surge of interest in industry and academia around so-called “graph-based” methods for high-dimensional near-neighbor search. Such methods include HNSW, DiskANN, and many others. While these methods differ in details, at a high level, they all find candidate near-neighbors by performing greedy search in a sparse graph constructed over the underlying vector data. While this approach works extremely well in practice, our theoretical understanding of why is limited. In this talk, I will discuss recent efforts to place graph-based methods on firmer theoretical ground by studying “graph navigability”, a widely adopted minimal necessary condition to ensure that greedy search finds good near-neighbors in the search graph. I will discuss existence results (when does a dataset admit a sparse navigable graph?) and algorithmic results (can we efficiently construct near-optimal navigable graphs?). I will also discuss open questions on navigability and graph-based search in general. The talk will be based on papers that will appear at NeurIPS 2025 and SODA 2026.