{"paper":{"title":"Query-Efficient Fixpoints of $\\ell_p$-Contractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.CC","authors_text":"Jonas Lill, Patrick Schnider, Sebastian Haslebacher, Simon Weber","submitted_at":"2025-03-20T12:30:34Z","abstract_excerpt":"We prove that an $\\epsilon$-approximate fixpoint of a map $f:[0,1]^d\\rightarrow [0,1]^d$ can be found with $\\mathcal{O}(d^2(\\log\\frac{1}{\\epsilon} + \\log\\frac{1}{1-\\lambda}))$ queries to $f$ if $f$ is $\\lambda$-contracting with respect to an $\\ell_p$-metric for some $p\\in [1,\\infty)\\cup\\{\\infty\\}$. This generalizes a recent result of Chen, Li, and Yannakakis [STOC'24] from the $\\ell_\\infty$-case to all $\\ell_p$-metrics. Previously, all query upper bounds for $p\\in [1,\\infty) \\setminus \\{2\\}$ were either exponential in $d$, $\\log\\frac{1}{\\epsilon}$, or $\\log\\frac{1}{1-\\lambda}$.\n  Chen, Li, and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.16089","kind":"arxiv","version":2},"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/2503.16089/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"}