{"paper":{"title":"Testing submodularity and other properties of valuation functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Abhinav Bommireddi, Eric Blais","submitted_at":"2016-11-23T16:51:08Z","abstract_excerpt":"We show that for any constant $\\epsilon > 0$ and $p \\ge 1$, it is possible to distinguish functions $f : \\{0,1\\}^n \\to [0,1]$ that are submodular from those that are $\\epsilon$-far from every submodular function in $\\ell_p$ distance with a constant number of queries.\n  More generally, we extend the testing-by-implicit-learning framework of Diakonikolas et al. (2007) to show that every property of real-valued functions that is well-approximated in $\\ell_2$ distance by a class of $k$-juntas for some $k = O(1)$ can be tested in the $\\ell_p$-testing model with a constant number of queries. This re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07879","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":""},"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"}