{"paper":{"title":"On the Complexity of Polytopes in $LI(2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Komei Fukuda, May Szedlak","submitted_at":"2017-06-30T10:51:58Z","abstract_excerpt":"In this paper we consider polytopes given by systems of $n$ inequalities in $d$ variables, where every inequality has at most two variables with nonzero coefficient. We denote this family by $LI(2)$. We show that despite of the easy algebraic structure, polytopes in $LI(2)$ can have high complexity. We construct a polytope in $LI(2)$, whose number of vertices is almost the number of vertices of the dual cyclic polytope, the difference is a multiplicative factor of depending on $d$ and in particular independent of $n$. Moreover we show that the dual cyclic polytope can not be realized in $LI(2)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.10114","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"}