{"paper":{"title":"Lower bounds for graph reconstruction with maximal independent set queries","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Alex Scott, Lukas Michel","submitted_at":"2024-04-04T14:25:21Z","abstract_excerpt":"We investigate the number of maximal independent set queries required to reconstruct the edges of a hidden graph. We show that randomised adaptive algorithms need at least $\\Omega(\\Delta^2 \\log(n / \\Delta) / \\log \\Delta)$ queries to reconstruct $n$-vertex graphs of maximum degree $\\Delta$ with success probability at least $1/2$, and we further improve this lower bound to $\\Omega(\\Delta^2 \\log(n / \\Delta))$ for randomised non-adaptive algorithms. We also prove that deterministic non-adaptive algorithms require at least $\\Omega(\\Delta^3 \\log n / \\log \\Delta)$ queries.\n  This improves bounds of K"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.03472","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/2404.03472/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"}