{"paper":{"title":"Wireless Expanders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David Peleg, Merav Parter, Shay Solomon, Shirel Attali","submitted_at":"2018-02-20T16:17:30Z","abstract_excerpt":"This paper introduces an extended notion of expansion suitable for radio networks. A graph $G=(V,E)$ is called an $(\\alpha_w, \\beta_w)$-{wireless expander} if for every subset $S \\subseteq V$ s.t. $|S|\\leq \\alpha_w \\cdot |V|$, there exists a subset $S'\\subseteq S$ s.t. there are at least $\\beta_w \\cdot |S|$ vertices in $V\\backslash S$ adjacent in $G$ to exactly one vertex in $S'$. The main question we ask is the following: to what extent are ordinary expanders also good {wireless} expanders? We answer this question in a nearly tight manner. On the positive side, we show that any $(\\alpha, \\bet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07177","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"}