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Recently, the problem of maximizing a DR-submodular function $f: \\mathbb{Z}_+^E \\rightarrow \\mathbb{R}_+$ subject to a budget constraint $\\|{\\bf x}\\|_1 \\leq B$ as well as additional constraints has received significant attention \\cite{SKIK14,SY15,MYK15,SY16}.\n  In this note, we give a generic reduction from the DR-submodular setting to the submodular setting. The running time of the reduction and t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.08362","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-06-27T16:44:44Z","cross_cats_sorted":["cs.AI","cs.LG"],"title_canon_sha256":"84f8cf3e9d709d60e38c45327b21e84884f3196453f8b2e83a6871de992bcd7e","abstract_canon_sha256":"f0c6399881069892e9ae6d5ae11a7046aba05df81ea737c5ae079ad8a97da34f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:57.411679Z","signature_b64":"tFVLHb1R5Q97LAA9LqqiL87rrCTsB4Q2396eMiFoDCSqAWzK2ApWNG4BK6AEOx/xZWOTtPewNRJBjMVyFNBJCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a26fa838d0e5a5d4299d07aa25512b6704a248b6bc181881461e092f9d663bc","last_reissued_at":"2026-05-18T00:14:57.410981Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:57.410981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Reduction for Optimizing Lattice Submodular Functions with Diminishing Returns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG"],"primary_cat":"cs.DS","authors_text":"Alina Ene, Huy L. Nguyen","submitted_at":"2016-06-27T16:44:44Z","abstract_excerpt":"A function $f: \\mathbb{Z}_+^E \\rightarrow \\mathbb{R}_+$ is DR-submodular if it satisfies $f({\\bf x} + \\chi_i) -f ({\\bf x}) \\ge f({\\bf y} + \\chi_i) - f({\\bf y})$ for all ${\\bf x}\\le {\\bf y}, i\\in E$. Recently, the problem of maximizing a DR-submodular function $f: \\mathbb{Z}_+^E \\rightarrow \\mathbb{R}_+$ subject to a budget constraint $\\|{\\bf x}\\|_1 \\leq B$ as well as additional constraints has received significant attention \\cite{SKIK14,SY15,MYK15,SY16}.\n  In this note, we give a generic reduction from the DR-submodular setting to the submodular setting. 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