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At one extreme, there is a trivial $2$-approximation for this problem that uses only $O(\\log n)$ space, namely, count the number of edges and output half of this value as the estimate for the size of the MAX-CUT. On the other extreme, for any fixed $\\epsilon > 0$, if one allows $\\tilde{O}(n)$ space, a $(1+\\epsilon)$-approximate solution to the MAX-CUT value can be obtained by storing an $\\tilde{O}(n)$-size sparsifier that essentially preserves MAX-CUT value.\n  Our main result is that an"},"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":"1811.10879","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-27T09:04:16Z","cross_cats_sorted":[],"title_canon_sha256":"d577d292aa7315c4a35061b513bf0945b6345268420828967ff27475d93b7f5b","abstract_canon_sha256":"037239876ea824129babf9855f264954a63e3db115c56d0dc8efc0ca023836f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:47.242045Z","signature_b64":"mTzRfj/xAafx/f/+bUjcRznpPxL8KXPszpsaHjsWcd6NGRO8lyZeUNRjLfRTDuVy1nef0Ynwifx1jFPT+hOiBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91ead2621b157426b3cfce0dda428b7158ee2c0fb3fa26f6da920db3879a65d1","last_reissued_at":"2026-05-17T23:59:47.241594Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:47.241594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Optimal Space Lower Bound for Approximating MAX-CUT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Dmitry Krachun, Michael Kapralov","submitted_at":"2018-11-27T09:04:16Z","abstract_excerpt":"We consider the problem of estimating the value of MAX-CUT in a graph in the streaming model of computation. 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