{"paper":{"title":"Towards a Converse for the Nearest Lattice Point Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Vinay A. Vaishampayan","submitted_at":"2017-11-13T17:26:03Z","abstract_excerpt":"Upper bounds on the communication complexity of finding the nearest lattice point in a given lattice $\\Lambda \\subset \\mathbb{R}^2$ was considered in earlier works~\\cite{VB:2017}, for a two party, interactive communication model. Here we derive a lower bound on the communication complexity of a key step in that procedure. Specifically, the problem considered is that of interactively finding $\\min(X_1,X_2)$, when $(X_1,X_2)$ is uniformly distributed on the unit square. A lower bound is derived on the single-shot interactive communication complexity and shown to be tight. This is accomplished by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04714","kind":"arxiv","version":3},"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"}