{"paper":{"title":"Single pass sparsification in the streaming model with edge deletions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ashish Goel, Ian Post, Michael Kapralov","submitted_at":"2012-03-22T07:45:13Z","abstract_excerpt":"In this paper we give a construction of cut sparsifiers of Benczur and Karger in the {\\em dynamic} streaming setting in a single pass over the data stream. Previous constructions either required multiple passes or were unable to handle edge deletions. We use $\\tilde{O}(1/\\e^2)$ time for each stream update and $\\tilde{O}(n/\\e^2)$ time to construct a sparsifier. Our $\\e$-sparsifiers have $O(n\\log^3 n/\\e^2)$ edges. The main tools behind our result are an application of sketching techniques of Ahn et al.[SODA'12] to estimate edge connectivity together with a novel application of sampling with limi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4900","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"}