{"paper":{"title":"Scaling Submodular Maximization via Pruned Submodularity Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","stat.ML"],"primary_cat":"cs.LG","authors_text":"Carlos Guestrin, Hua Ouyang, Jeff Bilmes, Tianyi Zhou, Yi Chang","submitted_at":"2016-06-01T18:58:36Z","abstract_excerpt":"We propose a new random pruning method (called \"submodular sparsification (SS)\") to reduce the cost of submodular maximization. The pruning is applied via a \"submodularity graph\" over the $n$ ground elements, where each directed edge is associated with a pairwise dependency defined by the submodular function. In each step, SS prunes a $1-1/\\sqrt{c}$ (for $c>1$) fraction of the nodes using weights on edges computed based on only a small number ($O(\\log n)$) of randomly sampled nodes. The algorithm requires $\\log_{\\sqrt{c}}n$ steps with a small and highly parallelizable per-step computation. An "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00399","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"}