{"paper":{"title":"New Notions and Constructions of Sparsification for Graphs and Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Luca Trevisan, Nikhil Bansal, Ola Svensson","submitted_at":"2019-05-04T13:58:37Z","abstract_excerpt":"A sparsifier of a graph $G$ (Bencz\\'ur and Karger; Spielman and Teng) is a sparse weighted subgraph $\\tilde G$ that approximately retains the cut structure of $G$. For general graphs, non-trivial sparsification is possible only by using weighted graphs in which different edges have different weights. Even for graphs that admit unweighted sparsifiers, there are no known polynomial time algorithms that find such unweighted sparsifiers.\n  We study a weaker notion of sparsification suggested by Oveis Gharan, in which the number of edges in each cut $(S,\\bar S)$ is not approximated within a multipl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01495","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"}