{"paper":{"title":"Generalized comparison trees for point-location problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CG","authors_text":"Daniel M Kane, Shachar Lovett, Shay Moran","submitted_at":"2018-04-23T03:46:20Z","abstract_excerpt":"Let $H$ be an arbitrary family of hyper-planes in $d$-dimensions. We show that the point-location problem for $H$ can be solved by a linear decision tree that only uses a special type of queries called \\emph{generalized comparison queries}. These queries correspond to hyperplanes that can be written as a linear combination of two hyperplanes from $H$; in particular, if all hyperplanes in $H$ are $k$-sparse then generalized comparisons are $2k$-sparse. The depth of the obtained linear decision tree is polynomial in $d$ and logarithmic in $|H|$, which is comparable to previous results in the lit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08237","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"}