{"paper":{"title":"Compressed Representation of Dynamic Binary Relations with Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ana Cerdeira-Pena, Gonzalo Navarro, Guillermo De Bernardo, Nieves R. Brisaboa","submitted_at":"2017-07-10T09:26:15Z","abstract_excerpt":"We introduce a dynamic data structure for the compact representation of binary relations $\\mathcal{R} \\subseteq A \\times B$. The data structure is a dynamic variant of the k$^2$-tree, a static compact representation that takes advantage of clustering in the binary relation to achieve compression. Our structure can efficiently check whether two objects $(a,b) \\in A \\times B$ are related, and list the objects of $B$ related to some $a \\in A$ and vice versa. Additionally, our structure allows inserting and deleting pairs $(a,b)$ in the relation, as well as modifying the base sets $A$ and $B$. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02769","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"}