{"paper":{"title":"Recognizing Generalized Transmission Graphs of Line Segments and Circular Sectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Katharina Klost, Wolfgang Mulzer","submitted_at":"2017-12-20T16:29:15Z","abstract_excerpt":"Suppose we have an arrangement $\\mathcal{A}$ of $n$ geometric objects $x_1, \\dots, x_n \\subseteq \\mathbb{R}^2$ in the plane, with a distinguished point $p_i$ in each object $x_i$. The generalized transmission graph of $\\mathcal{A}$ has vertex set $\\{x_1, \\dots, x_n\\}$ and a directed edge $x_ix_j$ if and only if $p_j \\in x_i$. Generalized transmission graphs provide a generalized model of the connectivity in networks of directional antennas.\n  The complexity class $\\exists \\mathbb{R}$ contains all problems that can be reduced in polynomial time to an existential sentence of the form $\\exists x_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07559","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"}