{"paper":{"title":"Almost Navigable Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Christopher Musco, Pratyush Avi","submitted_at":"2026-07-16T04:44:16Z","abstract_excerpt":"Graph-based methods like HNSW, DiskANN, NSG, and others have become an increasingly popular choice for implementing approximate nearest neighbor search (ANNS) in Vector Databases (VecDBs). The success of these methods has motivated the study of how to best construct a search graph for a given dataset. To that end, \\emph{navigability} has been identified as a desirable graph property which ensures good ANNS performance when combined with greedy search.\n  However, for a dataset with $n$ vectors, the sparsest navigable graph requires $O(n\\sqrt{n})$ edges in the worst-case, and we show empirically"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14564","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.14564/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}