{"paper":{"title":"On k-Column Sparse Packing Programs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aravind Srinivasan, Nikhil Bansal, Nitish Korula, Viswanath Nagarajan","submitted_at":"2009-08-16T17:55:03Z","abstract_excerpt":"We consider the class of packing integer programs (PIPs) that are column sparse, i.e. there is a specified upper bound k on the number of constraints that each variable appears in. We give an (ek+o(k))-approximation algorithm for k-column sparse PIPs, improving on recent results of $k^2\\cdot 2^k$ and $O(k^2)$. We also show that the integrality gap of our linear programming relaxation is at least 2k-1; it is known that k-column sparse PIPs are $\\Omega(k/ \\log k)$-hard to approximate. We also extend our result (at the loss of a small constant factor) to the more general case of maximizing a subm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2256","kind":"arxiv","version":3},"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"}