{"paper":{"title":"A Sketching Algorithm for Spectral Graph Sparsification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Bo Qin, David P. Woodruff, Jiecao Chen, Qin Zhang","submitted_at":"2014-12-28T23:22:42Z","abstract_excerpt":"We study the problem of compressing a weighted graph $G$ on $n$ vertices, building a \"sketch\" $H$ of $G$, so that given any vector $x \\in \\mathbb{R}^n$, the value $x^T L_G x$ can be approximated up to a multiplicative $1+\\epsilon$ factor from only $H$ and $x$, where $L_G$ denotes the Laplacian of $G$. One solution to this problem is to build a spectral sparsifier $H$ of $G$, which, using the result of Batson, Spielman, and Srivastava, consists of $O(n \\epsilon^{-2})$ reweighted edges of $G$ and has the property that simultaneously for all $x \\in \\mathbb{R}^n$, $x^T L_H x = (1 \\pm \\epsilon) x^T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8225","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"}