{"paper":{"title":"An SDP Relaxation for the Sparse Integer Least Squares Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.OC","authors_text":"Alberto Del Pia, Dekun Zhou","submitted_at":"2022-03-04T23:21:38Z","abstract_excerpt":"In this paper, we study the \\emph{sparse integer least squares problem} (SILS), an NP-hard variant of least squares with sparse $\\{0, \\pm 1\\}$-vectors. We propose an $\\ell_1$-based SDP relaxation, and a randomized algorithm for SILS, which computes feasible solutions with high probability with an asymptotic approximation ratio $1/T^2$ as long as the sparsity constant $\\sigma \\ll T$. Our algorithm handles large-scale problems, delivering high-quality approximate solutions for dimensions up to $d = 10,000$. The proposed randomized algorithm applies broadly to binary quadratic programs with a car"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.02607","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.02607/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}