{"id":1160501,"date":"2026-01-19T09:56:45","date_gmt":"2026-01-19T17:56:45","guid":{"rendered":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/?post_type=msr-research-item&#038;p=1160501"},"modified":"2026-01-19T09:56:45","modified_gmt":"2026-01-19T17:56:45","slug":"sort-before-you-prune-improved-worst-case-guarantees-of-the-diskann-family-of-graphs","status":"publish","type":"msr-research-item","link":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/publication\/sort-before-you-prune-improved-worst-case-guarantees-of-the-diskann-family-of-graphs\/","title":{"rendered":"Sort Before You Prune: Improved Worst-Case Guarantees of the DiskANN Family of Graphs"},"content":{"rendered":"<p>Graph-based data structures have become powerful and ubiquitous tools for scalable approximate nearest-neighbor (ANN) search over the past decade. In spite of their apparent practical performance, there has only recently been progress on the\u00a0<strong>worst-case<\/strong>\u00a0performance of these data structures. Indeed, the influential work of Indyx and Xu (2023) introduced the key concept of\u00a0-reachable graphs, showing that graphs constructed by the DiskANN algorithm (Subramanya, et. al. 2023) produce an\u00a0-approximate solution with a simple best-first search that runs in poly-logarithmic query time. In our work, we improve and generalize this analysis as follows: &#8211; We introduce\u00a0<strong>sorted<\/strong>\u00a0-reachable graphs, and use this notion to obtain a stronger approximation factor of\u00a0\u00a0for the DiskANN algorithm on Euclidean metrics. &#8211; We present the\u00a0<strong>first<\/strong>\u00a0worst-case theoretical analysis for the popular\u00a0<strong>beam-search<\/strong>\u00a0algorithm, which is used in practice to search these graphs for\u00a0\u00a0candidate nearest neighbors. We also present empirical results validating the significance of sorted\u00a0-reachable graphs, which aligns with our theoretical findings.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Graph-based data structures have become powerful and ubiquitous tools for scalable approximate nearest-neighbor (ANN) search over the past decade. In spite of their apparent practical performance, there has only recently been progress on the\u00a0worst-case\u00a0performance of these data structures. Indeed, the influential work of Indyx and Xu (2023) introduced the key concept of\u00a0-reachable graphs, showing that 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