{"paper":{"title":"Sparse Navigable Graphs for Nearest Neighbor Search: Algorithms and Hardness","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ashwin Padaki, Erik Waingarten, Sanjeev Khanna","submitted_at":"2025-07-18T16:41:21Z","abstract_excerpt":"We initiate the study of approximation algorithms and computational barriers for constructing sparse $\\alpha$-navigable graphs [IX23, DGM+24], a core primitive underlying recent advances in graph-based nearest neighbor search. Given an $n$-point dataset $P$ with an associated metric $\\mathsf{d}$ and a parameter $\\alpha \\geq 1$, the goal is to efficiently build the sparsest graph $G=(P, E)$ that is $\\alpha$-navigable: for every distinct $s, t \\in P$, there exists an edge $(s, u) \\in E$ with $\\mathsf{d}(u, t) < \\mathsf{d}(s, t)/\\alpha$. We consider two natural sparsity objectives: minimizing the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.14060","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/2507.14060/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"}