{"paper":{"title":"Faster Space-Efficient Algorithms for Subset Sum, k-Sum and Related Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CR"],"primary_cat":"cs.DS","authors_text":"Jesper Nederlof, Nikhil Bansal, Nikhil Vyas, Shashwat Garg","submitted_at":"2016-12-08T20:09:55Z","abstract_excerpt":"We present space efficient Monte Carlo algorithms that solve Subset Sum and Knapsack instances with $n$ items using $O^*(2^{0.86n})$ time and polynomial space, where the $O^*(\\cdot)$ notation suppresses factors polynomial in the input size. Both algorithms assume random read-only access to random bits. Modulo this mild assumption, this resolves a long-standing open problem in exact algorithms for NP-hard problems. These results can be extended to solve Binary Linear Programming on $n$ variables with few constraints in a similar running time. We also show that for any constant $k\\geq 2$, random"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02788","kind":"arxiv","version":2},"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"}