{"paper":{"title":"Adversarially Robust Approximate Furthest Neighbor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A data structure answers c-approximate furthest neighbor queries correctly against adaptive adversaries at query time Õ(min(d n^{1/c²}, n^{2/c²} + d)).","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Jeff Giliberti, Kiarash Banihashem, MohammadTaghi Hajiaghayi, Morteza Monemizadeh, Prashant Gokhale, Samira Goudarzi, Sandeep Silwal, Yuhao Liu","submitted_at":"2026-05-15T20:40:24Z","abstract_excerpt":"We work in the adaptive query model, where one is given a point set $P \\subset \\mathbb{R}^d$ and seeks to construct a data structure that can answer correctly and efficiently a sequence of adaptive queries. In this model, an adversary observes the answers returned by the data structure to previous queries $q_1, \\ldots, q_{i-1}$ and, based on this information, chooses the next query point $q_i$. This setting captures strong forms of adaptivity that naturally arise in modern machine learning pipelines, and rules out many classical randomized techniques that assume oblivious queries. Our focus is"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We present the first adversarially robust data structure for c-approximate furthest neighbor queries that achieves query time Õ(min(d n^{1/c²}, n^{2/c²} + d)).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The construction assumes a fixed point set P known in advance that can be preprocessed, and that the underlying distance computations and data-structure primitives (such as those from Indyk 2003) can be invoked in the stated time bounds under the adaptive adversary model.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"First adversarially robust data structure for c-approximate furthest neighbor search with query time matching the best known oblivious results for many parameter regimes.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A data structure answers c-approximate furthest neighbor queries correctly against adaptive adversaries at query time Õ(min(d n^{1/c²}, n^{2/c²} + d)).","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e8dc71dd876c5cb2013395e8b17d907eef13266ab8be62e95c22e16bf6811b53"},"source":{"id":"2605.16618","kind":"arxiv","version":1},"verdict":{"id":"ae9163bf-ac74-48f4-8377-64dc702eb37d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T21:12:06.987058Z","strongest_claim":"We present the first adversarially robust data structure for c-approximate furthest neighbor queries that achieves query time Õ(min(d n^{1/c²}, n^{2/c²} + d)).","one_line_summary":"First adversarially robust data structure for c-approximate furthest neighbor search with query time matching the best known oblivious results for many parameter regimes.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The construction assumes a fixed point set P known in advance that can be preprocessed, and that the underlying distance computations and data-structure primitives (such as those from Indyk 2003) can be invoked in the stated time bounds under the adaptive adversary model.","pith_extraction_headline":"A data structure answers c-approximate furthest neighbor queries correctly against adaptive adversaries at query time Õ(min(d n^{1/c²}, n^{2/c²} + d))."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16618/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T21:31:19.418839Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T21:21:28.522078Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:21:56.775625Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.589515Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"0068d257f9d170432d9697692c081d356be8235ccacf184c633c4ffba905ab31"},"references":{"count":73,"sample":[{"doi":"","year":2017,"title":"Ahle, T. D. Optimal las vegas locality sensitive data structures. In 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), pp.\\ 938--949. IEEE, 2017","work_id":"345dd021-67af-4053-b42d-6097cde9a993","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1145/3517804.3526228","year":2022,"title":"P., and Zhou, S","work_id":"801d365b-5a1e-4a1b-88d1-21a70d09385c","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"Adversarial laws of large numbers and optimal regret in online classification","work_id":"ee084163-bc91-49be-a303-f738994ace9e","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1992,"title":"Altman, N. S. An introduction to kernel and nearest-neighbor nonparametric regression. The American Statistician, 46 0 (3): 0 175--185, 1992","work_id":"540c1697-0464-4795-84bc-7fc1a3c157b7","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"C., Shiragur, K., and Xu, H","work_id":"7fe25e36-5acf-47eb-bc78-fde983d36a4e","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":73,"snapshot_sha256":"00ff7408c502f2ee1ce4247c81f15bbf87e1ee1d1823b19afcd4e1af119f6997","internal_anchors":2},"formal_canon":{"evidence_count":2,"snapshot_sha256":"9f1372e5f7c6de658dbe859a311c8abf0219032ec58e374f5db44eeaed7a6d83"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}